# American Institute of Mathematical Sciences

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 $\mathbb F_7$

 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.
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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