Near-Extremal Type I Self-Dual Codes with Minimal Shadow over GF (2) and GF (4)

Binary self-dual codes and additive self-dual codes over GF (4) contain common points. Both have Type I codes and Type II codes, as well as shadow codes. In this paper, we provide a comprehensive description of extremal and near-extremal Type I codes over GF (2) and GF (4) with minimal shadow. In particular, we prove that there is no near-extremal Type I [24m, 12m, 2m + 2] binary self-dual code with minimal shadow if m >= 323, and we prove that there is no near-extremal Type I (6m + 1, 2(6m+1), 2m + 1) additive self-dual code over GF (4) with minimal shadow if m >= 22.