New extremal binary self-dual codes of length 68

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Abidin Kaya¹  Bahattin Yildiz¹ 

[1] Department of Mathematics, Fatih University

关键词: Extremal codes;    Codes over rings;    Gray maps;    Quadratic double-circulant codes;   

DOI  :  10.13069/jacodesmath.79879

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

In this correspondence, we consider quadratic double and bordered double circulant construction methods over the ring R := F_2 + uF_2 + u^2F_2, where u^3 = 1. Among other examples, extremal binary self-dual codes of length 66 are obtained by these constructions. These are extended by using extension theorems for self-dual codes and as a result 8 new extremal binary self-dual codes of length 68 are obtained. More precisely, codes with beta=117, 120, 133 in W68;1 and with gamma = 1, beta=49, 57, 59 and codes with gamma=2, beta=69, 81 in W68;2 are constructed for the ?first time in the literature. In addition to these, some known such codes are reconstructed via this extension. The results are tabulated.

【 授权许可】

CC BY