erase.mag

压缩文件中是Error Correction Coding - Mathematical Methods and Algorithms(Wiley 2005)作者:(Todd K. Moon )的配

// test the erasure decoder

F<a> := FiniteField(16);
R<x> := PolynomialRing(F);

Gamma := (1-a^6*x)*(1-a^7*x);
t := 3;
f := 2;
j1 := 7;
j2 := 6;
Y1 := a^j1;
Y2 := a^j2;

rt := a^5*x^11 + a^6*x^9 + a^11*x^5 + x^4 + a^11*x^3 + a^6*x^2 + a^12;
// r(x) without the erasures in it

S1 := Evaluate(rt,a);
S2 := Evaluate(rt,a^2);
S3 := Evaluate(rt,a^3);
S4 := Evaluate(rt,a^4);
S5 := Evaluate(rt,a^5);
S6 := Evaluate(rt,a^6);

S := S1 + S2*x + S3*x^2 + S4*x^3 + S5*x^4 + S6*x^5;

Xi := (Gamma*S) mod x^(2*t);


// Run the Euclidean algorithm

aeuc := x^(2*t);
beuc := Xi;
nu := t + (f div 2);

// run the Euclidean alg
rm1 := aeuc;
ri := beuc;
sm1 := 1;
si := 0;
tm1 := 0;
ti := 1;

while(ri ne 0) do
   rm2 := rm1;
   rm1 := ri;
   tm2 := tm1;
   tm1 := ti;
   sm2 := sm1;
   sm1 := si;
   qi := rm2 div rm1;
   ri := rm2 mod rm1;
print ri;
   si := sm2 - qi*sm1;
   ti := tm2 - qi*tm1;
   if(Degree(ri) lt nu) then break; end if ;
end while;

ti;  // the error locator polynomial (not normalized)


Lambda := ti/Evaluate(ti,0);   // normalize so constant coeff. is 1
X1 := a^11;
Omega := (Lambda*Xi) mod x^(2*t);
Phi := (Lambda*Gamma);


e1 := Evaluate(Omega,X1^(-1))/Evaluate(Derivative(Phi),X1^(-1));
f1 := Evaluate(Omega,Y1^(-1))/Evaluate(Derivative(Phi),Y1^(-1));
f2 := Evaluate(Omega,Y2^(-1))/Evaluate(Derivative(Phi),Y2^(-1));