Neighborhoods of binary self-dual codes

Abstract

In this paper, we introduce the neighborhood of binary self-dual codes. Further, we show that for codelength divisible by 8 such a neighborhood consists of three self-dual codes, two of them are doubly-even and one is always singly-even. We investigate the relationship between neighboring codes. Finally, we prove that no better Type I code exists than the best possible Type II code of the same length.