Анализ временных характеристик кодера кодов Рида-Соломона

Таблица 2.

Сравнительная характеристика кодера кода Рида-Соломона для разных видов преобразования и для одинакового числа ошибок

Длина преобразования	Алгоритм кодирования	Количество исправляемых ошибок	Время работы, мс
	ОДПФ
	ОБПФ
	ОДПФ
	ОБПФ
	ОДПФ
	ОБПФ
	ОДПФ
	ОДПФ

Таблица 3.

Зависимость времени от количества ошибок при кодировании кода Рида-Соломона алгоритмом БПФ длины 255.

Количество исправляемых ошибок	Время работы, мс.

Таблица 4.

Зависимость времени от количества ошибок при кодировании кода Рида-Соломона алгоритмом ДПФ длины 255.

Количество исправляемых ошибок	Время работы, мс.

Таблица 5.

Зависимость времени от количества ошибок при кодировании кода Рида-Соломона алгоритмом ДПФ длины 85.

Количество исправляемых ошибок	Время работы, мс.

 

Таблица 6.

Зависимость времени, затраченного на вычисление ДПФ длины 255,от типа преобразования

Алгоритм	Время
ДПФ
Агарвала-Кули
БПФ

Приложение 2

Листинг программы

Модуль программного комплекса, реализующего построение поля , введение основных операций в этом поле, вычисление значения произвольного многочлена в любой точке поля, вычисление прямого и обратного ДПФ,ОДПФ, трехмерного преобразования Фурье и БПФ длин 255,3,5,17,15,51,85, кодирование вектора несистематическим кодом Рида-Соломона.

program GF2_8;

{$APPTYPE CONSOLE}

uses

SysUtils;

const n=255;

n1=8;

type m = packed array [1..n1] of char;

type Gal = array [0..n] of m;

type vect= array [0..n-1] of m;

type D3vect=array [0..2] of m;

type D5vect=array [0..4] of m;

type D17vect=array [0..16] of m;

type multPol=array [0..6] of m;

type deg3Pol=array [0..3] of m;

type degBig=array [0..18] of m;

type deg15Pol=array [0..15] of m;

type D85vect=array [0..84] of m;

type D51vect=array [0..50] of m;

type D15vect=array [0..14] of m;

//-----------------------

function plus(a,b:m):m;

var i: integer;

begin

for i:=1 to 8 do

if a[i]<>b[i] then plus[i]:='1'

else plus[i]:='0';

end;

//-----------------------

function LogZ(a:m; G:Gal): integer;

var i: integer;

label 1;

begin

if a='00000000' then LogZ:=-1 else begin

for i:=0 to n-1 do

if a=G[i] then begin LogZ:=i; goto 1; end;

end;

1:end;

//------------------------

function expZ(k: integer; A:Gal): m;

begin

if k=-1 then expZ:='00000000'

else

expZ:=A[k];

end;

//-----------------------

function mult(a,b:m; G:Gal):m;

var i,j,Log: integer;

begin

i:=LogZ(a,G);

j:=LogZ(b,G);

if (i=-1)or(j=-1) then mult:='00000000'

else begin Log:=(i+j) mod 255

mult:=expZ(Log,G);

end;

end;

//-----------------------

procedure Generate(var A:Gal);

var C7: m;

i,j:integer;

c:char;

fl: boolean;

begin

 

A[0]:='00000001';

C7:='00011101';

 

fl:= false;

for i:= 1 to n do

begin

c:=A[i-1,1];

if c = '1' then fl:= true;

for j:=1 to 8 do

A[i,j]:=A[i-1,j+1];

A[i,8]:='0';

if fl = true then begin

for j:= 1 to n1 do

if A[i, j] <> C7[j] then A[i, j]:='1' else A[i, j]:= '0';

fl:=false;

end;

end;

end;

//----------------------

function powZ(a:m; i:integer; G:gal):m;

var k,t: integer;

begin

if a='00000000' then powZ:='00000000' else begin //0^a=0

k:=LogZ(a,G);

t:=k*i mod 255;

powZ:=expZ(t,G);

end;

end;

//--------------------------------------------------

function dim3FUR(c:vect;G:gal):vect;

var i,j,k,t,t1,t2,t3: integer;

A,f3,f5,f17: array[0..16,0..4,0..2] of m;

temp,su,D,DD: m; it: integer;

begin

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

 

A[i,j,k]:=c[(85*k+51*j+120*i) mod 255];

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

su:='00000000';

for t:=0 to 2 do begin

DD:=powZ(G[85],t*k,G);

temp:=mult(A[i,j,t],DD,G);

su:=plus(su,temp);

end;

f3[i,j,k]:=su;

end;

for i:=0 to 16 do

for k:=0 to 2 do

for j:=0 to 4 do begin

su:='00000000';

for t:=0 to 4 do begin

DD:=powZ(G[51],t*j,G);

temp:=mult(f3[i,t,k],DD,G);

su:=plus(su,temp);

end;

f5[i,j,k]:=su;

end;

for j:=0 to 4 do

for k:=0 to 2 do

for i:=0 to 16 do begin

su:='00000000';

for t:=0 to 16 do begin

DD:=powZ(G[120],t*i,G);

temp:=mult(f5[t,j,k],DD,G);

su:=plus(su,temp);

end;

f17[i,j,k]:=su;

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do

dim3FUR[ (85*k+51*j+120*i) mod 255]:=f17[i,j,k];

end;

//-------------------------------------------------------------

function DPF256(c:vect;G:gal):vect;

var i,j: integer;

temp,r:m;

begin

for j:=0 to n-1 do begin

r:='00000000';

for i:=0 to n-1 do begin

temp:=mult(c[i],powZ(G[1],i*j,G),G);

r:=plus(temp,r);

end;

DPF256[j]:=r;

end;

end;

//-------------------------------------------------------------

function DPF256back(c:vect;G:gal):vect;

var i,j: integer;

temp,r:m;

begin

for j:=0 to n-1 do begin

r:='00000000';

for i:=0 to n-1 do begin

temp:=mult(c[i],powZ(G[254],i*j,G),G);

r:=plus(temp,r);

end;

DPF256back[j]:=r;

end;

end;

//------------------------------------------------------------------

function DPF17(c:D17vect;G:gal):d17vect

var i,j: integer;

temp,r:m;

begin

for j:=0 to 16 do begin

r:='00000000';

for i:=0 to 16 do begin

temp:=mult(c[i],powZ(G[120],i*j,G),G);

r:=plus(temp,r);

end;

DPF17[j]:=r;

end;

end;

//------------------------------------------------------------------

function DPF17back(c:D17vect;G:gal):d17vect;

var i,j: integer;

temp,r:m;

begin

for j:=0 to 16 do begin

r:='00000000';

for i:=0 to 16 do begin

temp:=mult(c[i],powZ(G[135],i*j,G),G);

r:=plus(temp,r);

end;

DPF17back[j]:=r;

end;

end;

//------------------------------------------------------------------

function DPF3(c:D3vect;G:gal):d3vect;

var i,j: integer;

temp,r:m;

begin

for j:=0 to 2 do begin

r:='00000000';

for i:=0 to 2 do begin

temp:=mult(c[i],powZ(G[85],i*j,G),G);

r:=plus(temp,r);

end;

DPF3[j]:=r;

end;

end;

//------------------------------------------------------------------

function DPF3back(c:D3vect;G:gal):d3vect;

var i,j: integer;

temp,r:m;

begin

for j:=0 to 2 do begin

r:='00000000';

for i:=0 to 2 do begin

temp:=mult(c[i],powZ(G[170],i*j,G),G);

r:=plus(temp,r);

end;

DPF3back[j]:=r;

end;

end;

//------------------------------------------------------------------

function DPF5(c:D5vect;G:gal):d5vect;

var i,j: integer;

temp,r:m;

begin

for j:=0 to 4 do begin

r:='00000000';

for i:=0 to 4 do begin

temp:=mult(c[i],powZ(G[51],i*j,G),G);

r:=plus(temp,r);

end;

DPF5[j]:=r;

end;

end;

//------------------------------------------------------------------

//------------------------------------------------------------------

function DPF5back(c:D5vect;G:gal):d5vect;

var i,j: integer;

temp,r:m;

begin

for j:=0 to 4 do begin

r:='00000000';

for i:=0 to 4 do begin

temp:=mult(c[i],powZ(G[204],i*j,G),G);

r:=plus(temp,r);

end;

DPF5back[j]:=r;

end;

end;

//------------------------------------------------------------------

function RootOfPol(pol:vect;root:m; G:gal):m;

var temp_v: vect;

sum: m;

i: integer;

begin

temp_v[0]:=pol[0];

 

for i:=1 to 254 do

if pol[i]<>'00000000' then

temp_v[i]:=mult(pol[i],powZ(root,i,G),G)

else temp_v[i]:='00000000';

sum:='00000000';

for i:=0 to 254 do

sum:=plus(sum,temp_v[i]);

RootOfPol:=sum;

end;

//-------------------------------------------------------------------

function RS_Encrypt(inf: vect; G:Gal):vect;

var i: integer;

begin

for i:=0 to 254 do

RS_Encrypt[i]:=RootOfPol(inf,G[255-i],G);

end;

//--------------------------------------------------------------------

procedure waste(DateTime,DateTime1:TDateTime);

var Hour,Min,Sec,Msec,Hour1,Min1,Sec1,Msec1:word;

Ms,sss:integer;

begin

decodetime(DateTime,Hour,Min,Sec,Msec); decodetime(DateTime1,Hour1,Min1,Sec1,Msec1);

ms:=Msec1-msec;

sss:=sec1-sec;

if ms<0 then begin

MS:=ms+1000;

SSS:=sss-1;

end;

writeln('algorithm waste is ',sss,' seconds, and ',ms{mod 65000},' milliseconds');

end;

//--------------------------------------------------------------------

function Dim3RPF(h:D3vect;G:Gal):D3vect;

var s1,m1,s2,tt: m;

begin

s1:=plus(h[1],h[2]);

m1:=mult(G[85],s1,G);

tt:=plus(h[0],s1);

s2:=plus(tt,m1);

Dim3RPF[1]:=plus(s2,h[1]);

Dim3RPF[2]:=plus(s2,h[2]);

Dim3RPF[0]:=tt;

end;

//--------------------------------------------------------------------

function Dim3RPFback(h:D3vect;G:Gal):D3vect;

var s1,m1,s2,tt: m;

begin

s1:=plus(h[1],h[2]);

m1:=mult(G[170],s1,G);

tt:=plus(h[0],s1);

s2:=plus(tt,m1);

Dim3RPFback[1]:=plus(s2,h[1]);

Dim3RPFback[2]:=plus(s2,h[2]);

Dim3RPFback[0]:=tt;

end;

//--------------------------------------------------------------------

function Dim5RPF(h:D5vect;G:Gal):D5vect;

var s1,s2,s3,s4,s5,m1,m2,m3,m4,m5,s6,s7,s8,s9,s10,s11,s12,tt: m;

begin

s1:=plus(h[2],h[3]);

s2:=plus(h[1],h[4]);

s3:=plus(h[1],h[3]);

s4:=plus(h[2],h[4]);

s5:=plus(s1,s2);

tt:=plus(s5,h[0]);

Dim5RPF[0]:=tt;

m1:=mult(plus(G[0],G[153]),s5,G);

m2:=mult(plus(G[153],G[204]),s1,G);

m3:=mult(plus(G[51],G[153]),s2,G);

m4:=mult(plus(G[51],G[204]),s3,G);

m5:=mult(plus(G[51],G[204]),s4,G);

s6:=plus(tt,m1);

s7:=plus(s6,m2);

s8:=plus(s6,m3);

s9:=plus(m5,h[2]);

s10:=plus(m4,h[1]);

s11:=plus(m5,h[4]);

s12:=plus(m4,h[3]);

Dim5RPF[1]:=plus(s8,s9);

Dim5RPF[2]:=plus(s7,s10);

Dim5RPF[3]:=plus(s7,s11);

Dim5RPF[4]:=plus(s8,s12);

end;

//--------------------------------------------------------------------

//--------------------------------------------------------------------

function Dim5RPFback(h:D5vect;G:Gal):D5vect;

var s1,s2,s3,s4,s5,m1,m2,m3,m4,m5,s6,s7,s8,s9,s10,s11,s12,tt: m;

begin

s1:=plus(h[2],h[3]);

s2:=plus(h[1],h[4]);

s3:=plus(h[1],h[3]);

s4:=plus(h[2],h[4]);

s5:=plus(s1,s2);

tt:=plus(s5,h[0]);

Dim5RPFback[0]:=tt;

m1:=mult(plus(G[0],G[102]),s5,G);

m2:=mult(plus(G[102],G[51]),s1,G);

m3:=mult(plus(G[204],G[102]),s2,G);

m4:=mult(plus(G[204],G[51]),s3,G);

m5:=mult(plus(G[204],G[51]),s4,G);

s6:=plus(tt,m1);

s7:=plus(s6,m2);

s8:=plus(s6,m3);

s9:=plus(m5,h[2]);

s10:=plus(m4,h[1]);

s11:=plus(m5,h[4]);

s12:=plus(m4,h[3]);

Dim5RPFback[1]:=plus(s8,s9);

Dim5RPFback[2]:=plus(s7,s10);

Dim5RPFback[3]:=plus(s7,s11);

Dim5RPFback[4]:=plus(s8,s12);

end;

//----------------------------

function multVaryOnVary(R,B:deg3Pol; G:Gal): multPol;

var s1,s2,s3,s4,s5,s6,m1,m2,m3,m4,s7,m5,m6,m7: m;

h0,h1,h2,h3,h4,h5,h6: m;

begin

s1:=plus(r[0],r[1]);

s2:=plus(r[0],r[2]); //s2:=plus(r[0],r[2]);

s3:=plus(r[1],r[3]);

s4:=plus(s2,s3);

s5:=plus(s4,s1);

h0:=mult(r[0],b[0],G);

m1:=mult(s1,plus(b[0],b[1]),G);

m2:=mult(r[1],b[1],G);

s6:=plus(h0,m2);

h1:=plus(s6,m1);

m3:=mult(r[2],b[2],G);

h6:=mult(r[3],b[3],G);

m4:=mult(s2,plus(b[0],b[2]),G);

h2:=plus(s6,plus(m3,m4));

s7:=plus(m3,h6);

m5:=mult(s3,plus(b[1],b[3]),G);

m6:=mult(s5,plus(b[2],b[3]),G);

m7:=mult(s4,plus(plus(b[0],b[1]),plus(b[2],b[3])),G);

h5:=plus(s7,m6);

h4:=plus(s7,plus(m2,m5));

h3:=plus(plus(h1,h5),plus(m4,plus(m5,m7)));

multVaryOnVary[0]:=h0;

multVaryOnVary[1]:=h1;

multVaryOnVary[2]:=h2;

multVaryOnVary[3]:=h3;

multVaryOnVary[4]:=h4;

multVaryOnVary[5]:=h5;

multVaryOnVary[6]:=h6;

end;

//--------------------------

function multFixonVary(r:deg3Pol;G:Gal):multPol;

begin

multFixonVary[0]:=plus(r[0],mult(r[0],G[85],G));

multFixonVary[1]:=plus(plus(r[0],r[1]),mult(r[1],G[85],G));

multFixonVary[2]:=plus(plus(r[1],r[2]),mult(plus(r[0],r[2]),G[85],G));

multFixonVary[3]:=plus(plus(r[0],r[2]),plus(r[3],mult(plus(r[1],r[3]),G[85],G)));

multFixonVary[4]:=plus(plus(r[1],r[3]),mult(r[2],G[85],G));

multFixonVary[5]:=plus(r[2],mult(r[3],G[85],G));

multFixonVary[6]:=r[3];

end;

//----------------------------------

function sumBigPol(H,P:degBig):degBig;

var i: integer;

begin

for i:=0 to 18 do

sumBigPol[i]:=plus(H[i],P[i]);

end;

//--------------------------

function sum3Pol(H,P:Deg3Pol):deg3Pol;

var i: integer;

begin

for i:=0 to 3 do

sum3Pol[i]:=plus(H[i],P[i]);

end;

//----------------------

function sumSmallPol(H,P:multPol):multPol;

var i: integer;

begin

for i:=0 to 6 do

sumSmallPol[i]:=plus(H[i],P[i]);

end;

//--------------------

function sum17Pol(H,P:D17Vect):D17Vect;

var i: integer;

begin

for i:=0 to 16 do

sum17Pol[i]:=plus(H[i],P[i]);

end;

//-------------------

function PxmoDD(P:DegBig): deg15Pol;

var i: integer;

begin

for i:=15 downto 3 do

PxmoDD[i]:=P[i];

PxmoDD[2]:=plus(P[2],P[18]);

PxmoDD[1]:=plus(P[1],P[17]);

PxmoDD[0]:=plus(P[0],P[16]);

end;

//---------------------

function mult15to15deg(U:deg15Pol;G:Gal):deg15pol;

var W:deg15pol; i:integer;

U1,U2,U3,U4:deg3Pol;

W1,W2,W3,W4:deg3Pol;

F1,F2,F3,F4:multPol;

Temp1,Temp3,Temp5,Temp6,Temp7,temp4:multPol;

Temp2:Deg3Pol;

temp8,temp9,temp10:multPol;

temp11,temp12,temp13,temp14,temp15,temp16:multPol;

temp17,temp18,temp19,temp20,temp21,temp22,temp23,temp24:multPol;

vec1,vec2,vec3,vec4:degBig;

FullPol: degBig;

begin

w[0]:=powZ(G[120],8,G);

w[1]:=powZ(G[120],6,G);

w[2]:=powZ(G[120],13,G);

w[3]:=powZ(G[120],14,G);

w[4]:=powZ(G[120],2,G);

w[5]:=powZ(G[120],10,G);

w[6]:=powZ(G[120],16,G);

w[7]:=powZ(G[120],12,G);

w[8]:=powZ(G[120],9,G);

w[9]:=powZ(G[120],11,G);

w[10]:=powZ(G[120],4,G);

w[11]:=powZ(G[120],3,G);

w[12]:=powZ(G[120],15,G);

w[13]:=powZ(G[120],7,G);

w[14]:=powZ(G[120],1,G);

w[15]:=powZ(G[120],5,G);

U1[0]:=U[0];

U1[1]:=U[1];

U1[2]:=U[2];

U1[3]:=U[3];

 

U2[0]:=U[4];

U2[1]:=U[5];

U2[2]:=U[6];

U2[3]:=U[7];

 

U3[0]:=U[8];

U3[1]:=U[9];

U3[2]:=U[10];

U3[3]:=U[11];

 

U4[0]:=U[12];

U4[1]:=U[13];

U4[2]:=U[14];

U4[3]:=U[15];

 

W1[0]:=W[0];

W1[1]:=W[1];

W1[2]:=W[2];

W1[3]:=W[3];

 

W2[0]:=W[4];

W2[1]:=W[5];

W2[2]:=W[6];

W2[3]:=W[7];

 

W3[0]:=W[8];

W3[1]:=W[9];

W3[2]:=W[10];

W3[3]:=W[11];

 

W4[0]:=W[12];

W4[1]:=W[13];

W4[2]:=W[14];

W4[3]:=W[15];

temp1:=multVaryOnVary(sum3Pol(U1,U2),sum3Pol(W1,W3),G); temp2:=sum3Pol(sum3Pol(U1,U2),sum3Pol(U3,U4));

temp3:=multVaryOnVary(temp2,W2,G);

temp4:=sumSmallPol(temp1,temp3);

temp5:=multVaryOnVary(sum3Pol(U1,U3),sum3Pol(W2,W3),G);

temp6:=multFixonVary(U2,G);

temp7:=sumSmallPol(temp4,temp5);

F1:=sumSmallPol(temp7,temp6);

temp8:=multVaryOnVary(sum3Pol(W1,W3),temp2,G);

temp9:=sumSmallPol(temp8,F1);

temp10:=multFixOnVary(sum3Pol(U2,U4),G);

F3:=sumSmallPol(temp10,temp9);

temp11:=multVaryOnVary(sum3Pol(U1,U2),sum3Pol(W1,W3),G);

temp12:=multVaryOnVary(temp2,sum3Pol(W1,sum3Pol(W2,W3)),G);

temp13:=sumSmallPol(temp11,temp12);

temp14:=multVaryOnVary(sum3Pol(U4,U2),sum3Pol(W1,W2),G);

temp15:=multFixOnVary(U3,G);

temp16:=sumSmallPol(temp14,Temp15);

F2:=sumSmallPol(temp16,temp13);

temp17:=multFixOnVary(temp2,G);

temp18:=multVaryOnVary(sum3Pol(U1,U2),sum3Pol(W1,W3),G);

temp19:=sumSmallPol(temp17,temp18);

temp20:=multVaryOnVary(temp2,W2,G);

temp21:=multVaryOnVary(sum3Pol(U2,U4),sum3Pol(W3,W4),G);

temp22:=sumSmallPol(temp21,temp20);

temp23:=sumSmallPol(temp22,temp19);

temp24:=multFixOnVary(U3,G);

F4:=sumSmallPol(temp24,temp23);

for i:=0 to 18 do begin

vec1[i]:='00000000';

vec2[i]:='00000000';

vec3[i]:='00000000';

vec4[i]:='00000000';

end;

vec1[0]:=F1[0];

vec1[1]:=F1[1];

vec1[2]:=F1[2];

vec1[3]:=F1[3];

vec1[4]:=F1[4];

vec1[5]:=F1[5];

vec1[6]:=F1[6];

//*x^4

vec2[4]:=F2[0];

vec2[5]:=F2[1];

vec2[6]:=F2[2];

vec2[7]:=F2[3];

vec2[8]:=F2[4];

vec2[9]:=F2[5];

vec2[10]:=F2[6];

//*x^8

vec3[8]:=F3[0];

vec3[9]:=F3[1];

vec3[10]:=F3[2];

vec3[11]:=F3[3];

vec3[12]:=F3[4];

vec3[13]:=F3[5];

vec3[14]:=F3[6];

//*x^12

vec4[12]:=F4[0];

vec4[13]:=F4[1];

vec4[14]:=F4[2];

vec4[15]:=F4[3];

vec4[16]:=F4[4];

vec4[17]:=F4[5];

vec4[18]:=F4[6];

FullPol:=sumBigPol(sumBigPol(vec1,vec2),sumBigPol(vec3,vec4));

mult15to15deg:=PxmoDD(FullPol);

end;

//-------------------

function mult15to15degobr(U:deg15Pol;G:Gal):deg15pol;

var W:deg15pol; i:integer;

U1,U2,U3,U4:deg3Pol;

W1,W2,W3,W4:deg3Pol;

F1,F2,F3,F4:multPol;

Temp1,Temp3,Temp5,Temp6,Temp7,temp4:multPol;

Temp2:Deg3Pol;

temp8,temp9,temp10:multPol;

temp11,temp12,temp13,temp14,temp15,temp16:multPol;

temp17,temp18,temp19,temp20,temp21,temp22,temp23,temp24:multPol;

vec1,vec2,vec3,vec4:degBig;

FullPol: degBig;

begin

w[0]:=powZ(G[135],8,G);

w[1]:=powZ(G[135],6,G);

w[2]:=powZ(G[135],13,G);

w[3]:=powZ(G[135],14,G);

w[4]:=powZ(G[135],2,G);

w[5]:=powZ(G[135],10,G);

w[6]:=powZ(G[135],16,G);

w[7]:=powZ(G[135],12,G);

w[8]:=powZ(G[135],9,G);

w[9]:=powZ(G[135],11,G);

w[10]:=powZ(G[135],4,G);

w[11]:=powZ(G[135],3,G);

w[12]:=powZ(G[135],15,G);

w[13]:=powZ(G[135],7,G);

w[14]:=powZ(G[135],1,G);

w[15]:=powZ(G[135],5,G);

 

U1[0]:=U[0];

U1[1]:=U[1];

U1[2]:=U[2];

U1[3]:=U[3];

 

U2[0]:=U[4];

U2[1]:=U[5];

U2[2]:=U[6];

U2[3]:=U[7];

 

U3[0]:=U[8];

U3[1]:=U[9];

U3[2]:=U[10];

U3[3]:=U[11];

 

U4[0]:=U[12];

U4[1]:=U[13];

U4[2]:=U[14];

U4[3]:=U[15];

 

W1[0]:=W[0];

W1[1]:=W[1];

W1[2]:=W[2];

W1[3]:=W[3];

 

W2[0]:=W[4];

W2[1]:=W[5];

W2[2]:=W[6];

W2[3]:=W[7];

 

W3[0]:=W[8];

W3[1]:=W[9];

W3[2]:=W[10];

W3[3]:=W[11];

 

W4[0]:=W[12];

W4[1]:=W[13];

W4[2]:=W[14];

W4[3]:=W[15];

temp1:=multVaryOnVary(sum3Pol(U1,U2),sum3Pol(W1,W3),G); temp2:=sum3Pol(sum3Pol(U1,U2),sum3Pol(U3,U4));

temp3:=multVaryOnVary(temp2,W2,G);

temp4:=sumSmallPol(temp1,temp3);

temp5:=multVaryOnVary(sum3Pol(U1,U3),sum3Pol(W2,W3),G);

temp6:=multFixonVary(U2,G);

temp7:=sumSmallPol(temp4,temp5);

F1:=sumSmallPol(temp7,temp6);

temp8:=multVaryOnVary(sum3Pol(W1,W3),temp2,G);

temp9:=sumSmallPol(temp8,F1);

temp10:=multFixOnVary(sum3Pol(U2,U4),G);

F3:=sumSmallPol(temp10,temp9);

temp11:=multVaryOnVary(sum3Pol(U1,U2),sum3Pol(W1,W3),G);

temp12:=multVaryOnVary(temp2,sum3Pol(W1,sum3Pol(W2,W3)),G);

temp13:=sumSmallPol(temp11,temp12);

temp14:=multVaryOnVary(sum3Pol(U4,U2),sum3Pol(W1,W2),G); temp15:=multFixOnVary(U3,G);

temp16:=sumSmallPol(temp14,Temp15);

F2:=sumSmallPol(temp16,temp13);

temp17:=multFixOnVary(temp2,G);

temp18:=multVaryOnVary(sum3Pol(U1,U2),sum3Pol(W1,W3),G);

temp19:=sumSmallPol(temp17,temp18);

temp20:=multVaryOnVary(temp2,W2,G);

temp21:=multVaryOnVary(sum3Pol(U2,U4),sum3Pol(W3,W4),G);

temp22:=sumSmallPol(temp21,temp20);

temp23:=sumSmallPol(temp22,temp19);

temp24:=multFixOnVary(U3,G);

F4:=sumSmallPol(temp24,temp23);

for i:=0 to 18 do begin

vec1[i]:='00000000';

vec2[i]:='00000000';

vec3[i]:='00000000';

vec4[i]:='00000000';

end;

//*x^0

vec1[0]:=F1[0];

vec1[1]:=F1[1];

vec1[2]:=F1[2];

vec1[3]:=F1[3];

vec1[4]:=F1[4];

vec1[5]:=F1[5];

vec1[6]:=F1[6];

//*x^4

vec2[4]:=F2[0];

vec2[5]:=F2[1];

vec2[6]:=F2[2];

vec2[7]:=F2[3];

vec2[8]:=F2[4];

vec2[9]:=F2[5];

vec2[10]:=F2[6];

//*x^8

vec3[8]:=F3[0];

vec3[9]:=F3[1];

vec3[10]:=F3[2];

vec3[11]:=F3[3];

vec3[12]:=F3[4];

vec3[13]:=F3[5];

vec3[14]:=F3[6];

//*x^12

vec4[12]:=F4[0];

vec4[13]:=F4[1];

vec4[14]:=F4[2];

vec4[15]:=F4[3];

vec4[16]:=F4[4];

vec4[17]:=F4[5];

vec4[18]:=F4[6];

FullPol:=sumBigPol(sumBigPol(vec1,vec2),sumBigPol(vec3,vec4));

mult15to15degobr:=PxmoDD(FullPol);

end;

//*****************************************************************************

function Dim17RPF(v:D17Vect; G: Gal):D17Vect;

var i: integer;

firstV: D17Vect;

secondV: deg15pol;

item: D17Vect;

res: D17Vect;

U: deg15pol;

s:m;

begin

s:='00000000';

for i:=0 to 16 do

s:=plus(s,v[i]);

FirstV[0]:=s;

for i:=1 to 16 do

FirstV[i]:=v[0];

U[0]:=v[5];

U[1]:=v[1];

U[2]:=v[7];

U[3]:=v[15];

U[4]:=v[3];

U[5]:=v[4];

U[6]:=v[11];

U[7]:=v[9];

U[8]:=v[12];

U[9]:=v[16];

U[10]:=v[10];

U[11]:=v[2];

U[12]:=v[14];

U[13]:=v[13];

U[14]:=v[6];

U[15]:=v[8];

secondV:=mult15to15deg(U,G);

 

item[0]:='00000000';

for i:=1 to 16 do

item[i]:=secondV[i-1];

res:=sum17Pol(item,firstV);

Dim17RPF[0]:=res[0];

Dim17RPF[5]:=res[1];

Dim17RPF[8]:=res[2];

Dim17RPF[6]:=res[3];

Dim17RPF[13]:=res[4];

Dim17RPF[14]:=res[5];

Dim17RPF[2]:=res[6];

Dim17RPF[10]:=res[7];

Dim17RPF[16]:=res[8];

Dim17RPF[12]:=res[9];

Dim17RPF[9]:=res[10];

Dim17RPF[11]:=res[11];

Dim17RPF[4]:=res[12];

Dim17RPF[3]:=res[13];

Dim17RPF[15]:=res[14];

Dim17RPF[7]:=res[15];

Dim17RPF[1]:=res[16];

end;

//*****************************************************************************

function Dim17RPFobr(v:D17Vect; G: Gal):D17Vect;

var i: integer;

firstV: D17Vect;

secondV: deg15pol;

item: D17Vect;

res: D17Vect;

U: deg15pol;

s:m;

begin

s:='00000000';

for i:=0 to 16 do

s:=plus(s,v[i]);

FirstV[0]:=s;

for i:=1 to 16 do

FirstV[i]:=v[0];

U[0]:=v[5];

U[1]:=v[1];

U[2]:=v[7];

U[3]:=v[15];

U[4]:=v[3];

U[5]:=v[4];

U[6]:=v[11];

U[7]:=v[9];

U[8]:=v[12];

U[9]:=v[16];

U[10]:=v[10];

U[11]:=v[2];

U[12]:=v[14];

U[13]:=v[13];

U[14]:=v[6];

U[15]:=v[8];

secondV:=mult15to15degobr(U,G);

 

item[0]:='00000000';

for i:=1 to 16 do

item[i]:=secondV[i-1];

res:=sum17Pol(item,firstV);

Dim17RPFobr[0]:=res[0];

Dim17RPFobr[5]:=res[1];

Dim17RPFobr[8]:=res[2];

Dim17RPFobr[6]:=res[3];

Dim17RPFobr[13]:=res[4];

Dim17RPFobr[14]:=res[5];

Dim17RPFobr[2]:=res[6];

Dim17RPFobr[10]:=res[7];

Dim17RPFobr[16]:=res[8];

Dim17RPFobr[12]:=res[9];

Dim17RPFobr[9]:=res[10];

Dim17RPFobr[11]:=res[11];

Dim17RPFobr[4]:=res[12];

Dim17RPFobr[3]:=res[13];

Dim17RPFobr[15]:=res[14];

Dim17RPFobr[7]:=res[15];

Dim17RPFobr[1]:=res[16];

end;

//--------------------

function RPF256(c:vect;G:Gal):vect;

var i,j,k,t: integer;

A,f3,f5,f17: array[0..16,0..4,0..2] of m;

temp:D3vect;

temp1:D5Vect;

fur2:D5vect;

fur1:D3Vect;

fur3:D17Vect;

temp2:D17Vect;

s:m;

r:integer;

begin

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

A[i,j,k]:=c[(85*k+51*j+120*i) mod 255];

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

temp[k]:=A[i,j,k];

if k=2 then begin

fur1:=dim3RPF(temp,G);

for t:=0 to 2 do

f3[i,j,t]:=fur1[t];

end;

end;

for i:=0 to 16 do

for k:=0 to 2 do

for j:=0 to 4 do begin

temp1[j]:=f3[i,j,k];

if j=4 then begin

fur2:=dim5RPF(temp1,G);

for t:=0 to 4 do

f5[i,t,k]:=fur2[t];

end;

end;

for j:=0 to 4 do

for k:=0 to 2 do

for i:=0 to 16 do begin

temp2[i]:=f5[i,j,k];

if i=16 then begin

fur3:=dim17RPF(temp2,G);

for t:=0 to 16 do

f17[t,j,k]:=fur3[t];

end;

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do

RPF256[ (85*k+51*j+120*i) mod 255]:=f17[i,j,k];

end;

//-----------------------------------------------------------------------------

function RPF256back(c:vect;G:Gal):vect;

var i,j,k,t: integer;

A,f3,f5,f17: array[0..16,0..4,0..2] of m;

temp:D3vect;

temp1:D5Vect;

fur2:D5vect;

fur1:D3Vect;

fur3:D17Vect;

temp2:D17Vect;

s:m;

r:integer;

begin

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

A[i,j,k]:=c[(85*k+51*j+120*i) mod 255];

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

temp[k]:=A[i,j,k];

if k=2 then begin

fur1:=dim3RPFback(temp,G);

for t:=0 to 2 do

f3[i,j,t]:=fur1[t];

end;

end;

for i:=0 to 16 do

for k:=0 to 2 do

for j:=0 to 4 do begin

temp1[j]:=f3[i,j,k];

if j=4 then begin

fur2:=dim5RPFback(temp1,G);

for t:=0 to 4 do

f5[i,t,k]:=fur2[t];

end;

end;

for j:=0 to 4 do

for k:=0 to 2 do

for i:=0 to 16 do begin

temp2[i]:=f5[i,j,k];

if i=16 then begin

fur3:=dim17RPFobr(temp2,G);

for t:=0 to 16 do

f17[t,j,k]:=fur3[t];

end;

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do

RPF256back[ (85*k+51*j+120*i) mod 255]:=f17[i,j,k];

end;

//-----------------------------------------------------------------------------

function DPF51(c:D51vect;G:gal):d51vect;

var i,j: integer;

temp,r:m;

ct,cs:vect;

begin

for i:=0 to n-1 do begin

if i mod 5=0 then ct[i]:=c[round(i/5)]

Else ct[i]:='00000000';

end;

for j:=0 to n-1 do begin

r:='00000000';

for i:=0 to n-1 do begin

temp:=mult(ct[i],powZ(G[1],i*j,G),G);

r:=plus(temp,r);

end;

cs[j]:=r;

end;

for i:=0 to n-1 do

if i mod 5=0 then dpf51[round(i/5)]:=cs[i];

end;

//-----------------------------------------------------------------------------

//-----------------------------------------------------------------------------

function DPF51back(c:D51vect;G:gal):d51vect;

var i,j: integer;

temp,r:m;

ct,cs:vect;

begin

for i:=0 to n-1 do begin

if i mod 5=0 then ct[i]:=c[round(i/5)]

Else ct[i]:='00000000';

end;

for j:=0 to n-1 do begin

r:='00000000';

for i:=0 to n-1 do begin

temp:=mult(ct[i],powZ(G[254],i*j,G),G);

r:=plus(temp,r);

end;

cs[j]:=r;

end;

for i:=0 to n-1 do

if i mod 5=0 then dpf51back[round(i/5)]:=cs[i];

end;

 

//-----------------------------------------------------------------------------

function DPF15(c:D15vect;G:gal):d15vect;

var i,j: integer;

temp,r:m;

ct,cs:vect;

begin

for i:=0 to n-1 do begin

if i mod 17=0 then ct[i]:=c[round(i/17)]

Else ct[i]:='00000000';

end;

for j:=0 to n-1 do begin

r:='00000000';

for i:=0 to n-1 do begin

temp:=mult(ct[i],powZ(G[1],i*j,G),G);

r:=plus(temp,r);

end;

cs[j]:=r;

end;

for i:=0 to n-1 do

if i mod 17=0 then dpf15[round(i/17)]:=cs[i];

end;

//-----------------------------------------------------------------------------

function DPF15back(c:D15vect;G:gal):d15vect;

var i,j: integer;

temp,r:m;

ct,cs:vect;

begin

for i:=0 to n-1 do begin

if i mod 17=0 then ct[i]:=c[round(i/17)]

Else ct[i]:='00000000';

end;

for j:=0 to n-1 do begin

r:='00000000';

for i:=0 to n-1 do begin

temp:=mult(ct[i],powZ(G[254],i*j,G),G);

r:=plus(temp,r);

end;

cs[j]:=r;

end;

for i:=0 to n-1 do

if i mod 17=0 then dpf15back[round(i/17)]:=cs[i];

end;

//--------------------

function RPF85(cd:d85vect;G:Gal):d85vect;

var i,j,k,t: integer;

A,f5,f17: array[0..16,0..4,0..2] of m;

temp1:D5Vect;

fur2:D5vect;

fur3:D17Vect;

temp2:D17Vect;

c:vect;

cr:vect;

begin

for i:=0 to n-1 do begin

if i mod 3=0 then c[i]:=cd[round(i/3)]

Else c[i]:='00000000';

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

f5[i,j,k]:='00000000';

f17[i,j,k]:='00000000';

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

A[i,j,k]:=c[(85*k+51*j+120*i) mod 255];

end;

 

for i:=0 to 16 do

for j:=0 to 4 do begin

temp1[j]:=A[i,j,0];

if j=4 then begin

fur2:=dim5RPF(temp1,G);

for t:=0 to 4 do

f5[i,t,0]:=fur2[t];

end;

end;

for j:=0 to 4 do

for i:=0 to 16 do begin

temp2[i]:=f5[i,j,0];

if i=16 then begin

fur3:=dim17RPF(temp2,G);

for t:=0 to 16 do

f17[t,j,0]:=fur3[t];

end;

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do

cr[ (85*k+51*j+120*i) mod 255]:=f17[i,j,k];

for i:=0 to n-1 do

if i mod 3=0 then rpf85[round(i/3)]:=cr[i];

end;

//-----------------------------------------------------------------------------

function RPF85back(cd:d85vect;G:Gal):d85vect;

var i,j,k,t: integer;

A,f5,f17: array[0..16,0..4,0..2] of m;

temp1:D5Vect;

fur2:D5vect;

fur3:D17Vect;

temp2:D17Vect;

c:vect;

cr:vect;

begin

for i:=0 to n-1 do begin

if i mod 3=0 then c[i]:=cd[round(i/3)]

Else c[i]:='00000000';

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

f5[i,j,k]:='00000000';

f17[i,j,k]:='00000000';

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

A[i,j,k]:=c[(85*k+51*j+120*i) mod 255];

end;

for i:=0 to 16 do

for j:=0 to 4 do begin

temp1[j]:=A[i,j,0];

if j=4 then begin

fur2:=dim5RPFback(temp1,G);

for t:=0 to 4 do

f5[i,t,0]:=fur2[t];

end;

end;

for j:=0 to 4 do

for i:=0 to 16 do begin

temp2[i]:=f5[i,j,0];

if i=16 then begin

fur3:=dim17RPFobr(temp2,G);

for t:=0 to 16 do

f17[t,j,0]:=fur3[t];

end;

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do

cr[ (85*k+51*j+120*i) mod 255]:=f17[i,j,k];

for i:=0 to n-1 do

if i mod 3=0 then rpf85back[round(i/3)]:=cr[i];

end;

//-----------------------------------------------------------------------------

function DPF85(c:D85vect;G:gal):d85vect;

var i,j: integer;

temp,r:m;

ct,cs:vect;

begin

for i:=0 to n-1 do begin

if i mod 3=0 then ct[i]:=c[round(i/3)]

Else ct[i]:='00000000';

end;

for j:=0 to n-1 do begin

r:='00000000';

for i:=0 to n-1 do begin

temp:=mult(ct[i],powZ(G[1],i*j,G),G);

r:=plus(temp,r);

end;

cs[j]:=r;

end;

//íàçàä

for i:=0 to n-1 do

if i mod 3=0 then dpf85[round(i/3)]:=cs[i];

end;

//------------------------------------------------------------------------------

function DPF85back(c:D85vect;G:gal):d85vect;

var i,j: integer;

temp,r:m;

ct,cs:vect;

begin

for i:=0 to n-1 do begin

if i mod 3=0 then ct[i]:=c[round(i/3)]

Else ct[i]:='00000000';

end;

for j:=0 to n-1 do begin

r:='00000000';

for i:=0 to n-1 do begin

temp:=mult(ct[i],powZ(G[254],i*j,G),G);

r:=plus(temp,r);

end;

cs[j]:=r;

end;

//íàçàä

for i:=0 to n-1 do

if i mod 3=0 then dpf85back[round(i/3)]:=cs[i];

end;

//--------------------

function RPF51(cd:d51vect;G:Gal):d51vect;

var i,j,k,t: integer;

A,f3,f17: array[0..16,0..4,0..2] of m;

temp:D3vect;

fur1:D3Vect;

fur3:D17Vect;

temp2:D17Vect;

c,cr:vect;

begin

for i:=0 to n-1 do begin

if i mod 5=0 then c[i]:=cd[round(i/5)]

Else c[i]:='00000000';

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

f3[i,j,k]:='00000000';

f17[i,j,k]:='00000000';

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

A[i,j,k]:=c[(85*k+51*j+120*i) mod 255];

end;

for i:=0 to 16 do

for k:=0 to 2 do begin

temp[k]:=A[i,0,k];

if k=2 then begin

fur1:=dim3RPF(temp,G);

for t:=0 to 2 do

f3[i,0,t]:=fur1[t];

end;

end;

for k:=0 to 2 do

for i:=0 to 16 do begin

temp2[i]:=f3[i,0,k];

if i=16 then begin

fur3:=dim17RPF(temp2,G);

for t:=0 to 16 do

f17[t,0,k]:=fur3[t];

end;

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do

cr[ (85*k+51*j+120*i) mod 255]:=f17[i,j,k];

for i:=0 to n-1 do

if i mod 5=0 then rpf51[round(i/5)]:=cr[i];

end;

//------------------------------------------------------------------------------

function RPF51back(cd:d51vect;G:Gal):d51vect;

var i,j,k,t: integer;

A,f3,f17: array[0..16,0..4,0..2] of m;

temp:D3vect;

fur1:D3Vect;

fur3:D17Vect;

temp2:D17Vect;

c,cr:vect;

begin

for i:=0 to n-1 do begin

if i mod 5=0 then c[i]:=cd[round(i/5)]

Else c[i]:='00000000';

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

f3[i,j,k]:='00000000';

f17[i,j,k]:='00000000';

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

A[i,j,k]:=c[(85*k+51*j+120*i) mod 255];

end;

for i:=0 to 16 do

for k:=0 to 2 do begin

temp[k]:=A[i,0,k];

if k=2 then begin

fur1:=dim3RPFback(temp,G);

for t:=0 to 2 do

f3[i,0,t]:=fur1[t];

end;

end;

for k:=0 to 2 do

for i:=0 to 16 do begin

temp2[i]:=f3[i,0,k];

if i=16 then begin

fur3:=dim17RPFobr(temp2,G);

for t:=0 to 16 do

f17[t,0,k]:=fur3[t];

end;

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do

cr[ (85*k+51*j+120*i) mod 255]:=f17[i,j,k];

for i:=0 to n-1 do

if i mod 5=0 then rpf51back[round(i/5)]:=cr[i];

end;

//--------------------

function RPF15(cd:d15vect;G:Gal):d15vect;

var i,j,k,t: integer;

A,f3,f5: array[0..16,0..4,0..2] of m;

temp:D3vect;

temp1:D5Vect;

fur2:D5vect;

fur1:D3Vect;

c,cr:vect;

begin

for i:=0 to n-1 do begin

if i mod 17=0 then c[i]:=cd[round(i/17)]

Else c[i]:='00000000';

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

f3[i,j,k]:='00000000';

f5[i,j,k]:='00000000';

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

A[i,j,k]:=c[(85*k+51*j+120*i) mod 255];

end;

for j:=0 to 4 do

for k:=0 to 2 do begin

temp[k]:=A[0,j,k];

if k=2 then begin

fur1:=dim3RPF(temp,G);

for t:=0 to 2 do

f3[0,j,t]:=fur1[t];

end;

end;

for k:=0 to 2 do

for j:=0 to 4 do begin

temp1[j]:=f3[0,j,k];

if j=4 then begin

fur2:=dim5RPF(temp1,G);

for t:=0 to 4 do

f5[0,t,k]:=fur2[t];

end;

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do

cr[ (85*k+51*j+120*i) mod 255]:=f5[i,j,k];

for i:=0 to n-1 do

if i mod 17=0 then rpf15[round(i/17)]:=cr[i];

end;

//-----------------------------------------------------------------------------

function RPF15back(cd:d15vect;G:Gal):d15vect;

var i,j,k,t: integer;

A,f3,f5: array[0..16,0..4,0..2] of m;

temp:D3vect;

temp1:D5Vect;

fur2:D5vect;

fur1:D3Vect;

c,cr:vect;

begin

for i:=0 to n-1 do begin

if i mod 17=0 then c[i]:=cd[round(i/17)]

Else c[i]:='00000000';

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

f3[i,j,k]:='00000000';

f5[i,j,k]:='00000000';

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do begin

A[i,j,k]:=c[(85*k+51*j+120*i) mod 255];

end;

for j:=0 to 4 do

for k:=0 to 2 do begin

temp[k]:=A[0,j,k];

if k=2 then begin

fur1:=dim3RPFback(temp,G);

for t:=0 to 2 do

f3[0,j,t]:=fur1[t];

end;

end;

for k:=0 to 2 do

for j:=0 to 4 do begin

temp1[j]:=f3[0,j,k];

if j=4 then begin

fur2:=dim5RPFback(temp1,G);

for t:=0 to 4 do

f5[0,t,k]:=fur2[t];

end;

end;

for i:=0 to 16 do

for j:=0 to 4 do

for k:=0 to 2 do

cr[ (85*k+51*j+120*i) mod 255]:=f5[i,j,k];

for i:=0 to n-1 do

if i mod 17=0 then rpf15back[round(i/17)]:=cr[i];

end;