Abstract
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.
Highlights
Let F2 = {0, 1} be the finite field of two elements and F4 = {0, 1, ω, ω 2 } be the finite field of four elements where ω 2 = ω + 1
An additive (n, 2k ) F4 -code C is a code of length n which contains 2k codewords
All additive circulant graph codes of length 13 ≤ n ≤ 29 and 31 ≤ n ≤ 33 having the largest minimum weight were classified by Varbanov [10]
Summary
An additive (n, 2k ) F4 -code having minimum weight d is called an additive (n, 2k , d) F4 -code. Additive F4 -codes of length n were classified by using n × n adjacency matrices of graphs for 1 ≤ n ≤ 12, by Danielsen and Parker [5]. Varbanov [10] constructed some self-dual additive F4 -codes from adjacency matrices of circulant graphs. All additive circulant graph codes of length 13 ≤ n ≤ 29 and 31 ≤ n ≤ 33 having the largest minimum weight were classified by Varbanov [10]. All bordered circulant graph codes of length n = 2, 3, 6, 8, 9, 14, 15, 18, 20, 22 having the largest minimum weight were classified by Danielsen and Parker [6]. All computer calculations were done using Magma [2]
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