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May  2007, 1(2): 223-238. doi: 10.3934/amc.2007.1.223

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

T. Aaron Gulliver 1, , Masaaki Harada 2, and  Hiroki Miyabayashi 2,

1. 

Department of Electrical and Computer Engineering, University of Victoria, P. O. Box 3055, STN CSC, Victoria, B. C., Canada V8W 3P6, Canada
2. 

Department of Mathematical Sciences, Yamagata University, Yamagata 990–8560, Japan, Japan

Received  October 2006 Revised  January 2007 Published  May 2007

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.
Keywords: double circulant code, quasi-twisted code., Self-dual code.
Mathematics Subject Classification: 94B0.
Citation: T. Aaron Gulliver, Masaaki Harada, Hiroki Miyabayashi. Double circulant and quasi-twisted self-dual codes over $\mathbb F_5$ and $\mathbb F_7$. Advances in Mathematics of Communications, 2007, 1 (2) : 223-238. doi: 10.3934/amc.2007.1.223
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