proposition: Lemma O_in_codebook : 0 \in codebook.
proof: Proof. rewrite inE; apply/forallP => i; apply/implyP => i0; by rewrite fdcoor0. Qed.
imports: mathcomp(all_ssreflect ssralg finalg poly polydiv cyclic) mathcomp(perm matrix mxpoly vector mxalgebra zmodp) ssr_ext ssralg_ext poly_ext channel_code decoding linearcode hamming dft poly_decoding euclid grs cyclic_code