Nonexistence of Several Infinite Families of Binary Self-Orthogonal Codes
Shitao Li, Minjia Shi, Tor Helleseth, San Ling · IEEE Transactions on Information Theory · 2025
The existence of optimal binary self-orthogonal codes has been well characterized. In this paper, we develop general methods involving residual codes and the MacWilliams identities to prove the nonexistence of several infinite families of binary self-orthogonal codes, despite the existence of binary linear codes with the same parameters. In particular, we focus on the largest minimum distances of optimal binary self-orthogonal codes with dimension eight.