proposition: Lemma enc_img_is_code : (enc channel_code) @: [finType of 'rV_(n - m)] \subset Hamming.code m.
proof: Proof. apply/subsetP => /= t /imsetP[/= x _] ->. by rewrite mem_kernel_syndrome0 (syndrome_enc x). 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