Transforms

Contents

Mattson--Solomon Transforms

MattsonSolomonTransform(f, n) : RngUPolElt, RngIntElt -> RngUPolElt
Given f, a polynomial over a finite field containing a primitive n-th root of unity, return the Mattson--Solomon transform of parameter n.
InverseMattsonSolomonTransform(A, n) : RngUPolElt, RngIntElt -> RngUPolElt
Given A, a polynomial over a finite field containing a primitive n-th root of unity, return the inverse Mattson--Solomon transform of parameter n.

Example CodeFld_MattsonSolomonTransform (H161E48)

We compute the Mattson--Solomon transform of parameter n=7 of the polynomial x4 + x2 + x + 1 over GF(212).
> n := 7;
> K := GF(2, 12);
> FP<x> := PolynomialRing(K);
> f := x^4 + x^2 + x + 1;
> A := MattsonSolomonTransform(f, n);
> A;
x^6 + x^5 + x^3

Krawchouk Polynomials

KrawchoukPolynomial(K, n, k) : FldFin, RngIntElt, RngIntElt -> RngUPolElt
Return the Krawchouk polynomial of parameters k and n in K over the rational field.
KrawchoukTransform(f, K, n) : RngUPolElt, FldFin, RngIntElt -> RngUPolElt
Return the Krawchouk transform of the polynomial f over the rational field with respect to the vector space Kn.
InverseKrawchouk(A, K, n) : RngUPolElt, FldFin, RngIntElt -> RngUPolElt
Return the inverse Krawchouk transform of the polynomial A over the rational field with respect to the vector space Kn.
V2.28, 13 July 2023