fact: Definition codebook := [set \row_i ((rVpoly f).[a ``_ i] * (b ``_ i)) | f in 'rV[F]_k].
imports: mathcomp(all_ssreflect ssralg finalg poly polydiv cyclic) mathcomp(perm matrix mxpoly vector mxalgebra zmodp) ssr_ext ssralg_ext vandermonde linearcode dft poly_decoding