Neighborhoods of binary self-dual codes (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.