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

Information

Sunghyu Han¹ 

[1] School of Liberal Arts, KoreaTech, Cheonan 31253, Korea;

关键词: additive codes over GF(4);    binary codes;    extremal codes;    minimal shadow;    near-extremal codes;    self-dual codes;   

DOI  :  10.3390/info9070172

来源: DOAJ

【 摘 要 】

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+1,26m+1,2m+1) additive self-dual code over GF(4) with minimal shadow if m≥22.

【 授权许可】

Unknown