proposition: Lemma syndrome_enc msg : syndrome (Hamming.PCM m) ((enc channel_code) msg) = 0.
proof: Proof. apply/eqP => /=; rewrite ffunE /syndrome. by rewrite trmx_mul trmxK -mulmxA -(trmxK GEN) -trmx_mul PCM_GEN trmx0 mulmx0. Qed.
imports: mathcomp(all_ssreflect ssralg fingroup finalg perm zmodp) mathcomp(matrix mxalgebra vector) mathcomp(Rstruct) realType_ext ssr_ext ssralg_ext f2 linearcode natbin ssrR hamming bigop_ext fdist proba channel channel_code decoding binary_symmetric_channel