Journal of Algebra Combinatorics Discrete Structures and Applications | |
New extremal binary self-dual codes of length 68 | |
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
【 预 览 】
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