Double circulant and quasi-twisted self-dual codes over $\mathbb F_5$ and $\mathbb F_7$

T. Aaron Gulliver; Masaaki Harada; Hiroki Miyabayashi

doi:10.3934/amc.2007.1.223

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2007, Volume 1, Issue 2: 223-238. Doi: 10.3934/amc.2007.1.223

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Double circulant and quasi-twisted self-dual codes over $\mathbb F_5$ and $\mathbb F_7$

1.
Department of Electrical and Computer Engineering, University of Victoria, P. O. Box 3055, STN CSC, Victoria, B. C., Canada V8W 3P6
2.
Department of Mathematical Sciences, Yamagata University, Yamagata 990–8560

Received: September 30, 2006

Revised: December 31, 2006

Published: June 2007

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Abstract

In this paper, we consider double circulant and quasi-twisted selfdual codes over $\mathbb F_5$ and $\mathbb F_7$. We determine the highest minimum weights for such codes of lengths up to 34 for $\mathbb F_5$ and up to 28 for $\mathbb F_7$, and classify the codes with these minimum weights. In particular, we give a double circulant self-dual [32, 16] code over $\mathbb F_5$ which has a higher minimum weight than the previously best known linear code with these parameters. In addition, a self-dual code over $\mathbb F_7$ is presented which has a higher minimum weight than the previously best known self-dual code for length 28.

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Mathematics Subject Classification: 94B05.

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