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New extremal binary self-dual codes of length 68
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.
Keywords
References
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- A. Kaya, B. Yildiz, Binary generator matrices of new extremal self-dual binary codes of length 68, available online at http://www.fatih.edu.tr/~akaya/binary/68u31.txt
- A. Kaya, B. Yildiz, Extension theorems for self-dual codes over rings and new binary self-dual codes, available online at http://arxiv.org/abs/1404.0195.
Details
Primary Language
English
Subjects
-
Journal Section
-
Publication Date
March 1, 2014
Submission Date
January 22, 2015
Acceptance Date
-
Published in Issue
Year 2014 Volume: 1 Number: 1
APA
Kaya, A., & Yildiz, B. (2014). New extremal binary self-dual codes of length 68. Journal of Algebra Combinatorics Discrete Structures and Applications, 1(1), 29-39. https://doi.org/10.13069/jacodesmath.79879
AMA
1.Kaya A, Yildiz B. New extremal binary self-dual codes of length 68. Journal of Algebra Combinatorics Discrete Structures and Applications. 2014;1(1):29-39. doi:10.13069/jacodesmath.79879
Chicago
Kaya, Abidin, and Bahattin Yildiz. 2014. “New Extremal Binary Self-Dual Codes of Length 68”. Journal of Algebra Combinatorics Discrete Structures and Applications 1 (1): 29-39. https://doi.org/10.13069/jacodesmath.79879.
EndNote
Kaya A, Yildiz B (March 1, 2014) New extremal binary self-dual codes of length 68. Journal of Algebra Combinatorics Discrete Structures and Applications 1 1 29–39.
IEEE
[1]A. Kaya and B. Yildiz, “New extremal binary self-dual codes of length 68”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 1, no. 1, pp. 29–39, Mar. 2014, doi: 10.13069/jacodesmath.79879.
ISNAD
Kaya, Abidin - Yildiz, Bahattin. “New Extremal Binary Self-Dual Codes of Length 68”. Journal of Algebra Combinatorics Discrete Structures and Applications 1/1 (March 1, 2014): 29-39. https://doi.org/10.13069/jacodesmath.79879.
JAMA
1.Kaya A, Yildiz B. New extremal binary self-dual codes of length 68. Journal of Algebra Combinatorics Discrete Structures and Applications. 2014;1:29–39.
MLA
Kaya, Abidin, and Bahattin Yildiz. “New Extremal Binary Self-Dual Codes of Length 68”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 1, no. 1, Mar. 2014, pp. 29-39, doi:10.13069/jacodesmath.79879.
Vancouver
1.Abidin Kaya, Bahattin Yildiz. New extremal binary self-dual codes of length 68. Journal of Algebra Combinatorics Discrete Structures and Applications. 2014 Mar. 1;1(1):29-3. doi:10.13069/jacodesmath.79879
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