Abstract :
The trellis complexity s(C) of an [n, k, d]-code C is investigated, in the case where the weights of nonzero codewords in C are confined to {d, ···, 2d-1}∪{n}. It is shown that s(C)⩾k-1. Furthermore, s(C)=k-1 if the code is self-complementary. If the nonzero weights are confined to {d, ···, 2d-3}, then s(C)=k
Keywords :
binary sequences; block codes; computational complexity; directed graphs; linear codes; binary linear block codes; directed graph; nonzero codewords; nonzero weights; self-complementary code; trellis complexity; Binary codes; Block codes; Councils; Decoding; Hamming weight; Informatics; Linear code; Maximum likelihood decoding; State-space methods; Tin; Vectors; Viterbi algorithm;
