Cyclic Self-Dual Codes1
نویسندگان
چکیده
(in this paper all codes are binary and linear). But, as we shall see in Section III, there exist nontrivial cyclic self-dual codes, the shortest of which has length 14. On the other hand there do not exist doubly-even cyclic self-dual codes, i.e. codes in which all weights are divisible by 4. This is a consequence of Theorem 1. Theorem 1. Suppose C is a binary self-dual code of length n, where n = 2a · b, a ≥ 1, b ≥ 1 and b is odd, that is fixed (setwise) by a permutation group G satisfying the conditions (a) G is transitive A slightly different version of this paper appeared in IEEE Trans. Information Theory, 29 (1983), 364–366.
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