Double Circulant Self-Dual Codes From Generalized Cyclotomic Classes Modulo 2p

11/14/2019

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by   Tongjiang Yan, et al.

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In this paper, constructions of some double circulant self-dual codes by generalized cyclotomic classes modulo 2p in terms of the theory of Galois rings , where p is an odd prime. This technique is applied to [12, 6, 4] and [44, 22, 8] binary self-dual codes to obtain optimal self-dual codes over GF(2). This paper also shows that the corresponding length 28 code contains a weight 9 codeword over GF(4) and thus is highest known. Based on the properties of generalized cyclotomy, some of these codes can be proved to possess good minimum weights.