Transforms

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: Mattson-Solomon Transform (ex-15eadc)

We compute the Mattson–Solomon transform of parameter \(n=7\) of the polynomial \(x^4 + x^2 + x + 1\) over \({\bf F}_{2^{12}}\).

> 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

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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 \(K^n\).

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 \(K^n\).