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New extremal binary self-dual codes of length 68
2014
Journal:  
Journal of Algebra Combinatorics Discrete Structures and Applications
Author:  
DOI:  
10.13069/jacodesmath.79879
Abstract:

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.

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Journal of Algebra Combinatorics Discrete Structures and Applications

Field :   Fen Bilimleri ve Matematik; Mühendislik

Journal Type :   Uluslararası

Metrics
Article : 169
Cite : 4
Details
Journal of Algebra Combinatorics Discrete Structures and Applications