Neighborhoods of binary self-dual codes

Published 11 Jun 2022 in cs.IT, cs.DM, and math.IT | (2206.05588v2)

Abstract: In this paper, we introduce and investigate the neighborhood of binary self-dual codes. We prove that there is no better Type I code than the best Type II code of the same length. Further, we give some new necessary conditions for the existence of a singly-even $(56,28,12)$-code and a doubly-even $(72,36,16)$-code.

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