Self-dual additive $ \mathbb{F}_4 $-codes of lengths up to 40 represented by circulant graphs | Zendy

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Self-dual additive $ \mathbb{F}_4 $-codes of lengths up to 40 represented by circulant graphs

Author(s) -

Ken Saito

Publication year - 2019

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2019014

Subject(s) - circulant matrix , mathematics , circulant graph , combinatorics , minimum weight , graph , discrete mathematics , dual (grammatical number) , line graph , voltage graph , art , literature

In this paper, we consider additive circulant graph codes which are self-dual additive \begin{document}$ \mathbb{F}_4 $\end{document} -codes. We classify all additive circulant graph codes of length \begin{document}$ n = 30, 31 $\end{document} and \begin{document}$ 34 \le n \le 40 $\end{document} having the largest minimum weight. We also classify bordered circulant graph codes of lengths up to 40 having the largest minimum weight.

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