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August  2007, 1(3): 357-398. doi: 10.3934/amc.2007.1.357

Additive self-dual codes over $\mathbb F_4$ with an automorphism of odd prime order

W. Cary Huffman 1,

1. 

Department of Mathematics and Statistics, Loyola University, Chicago, IL 60626, United States

Received  April 2007 Revised  June 2007 Published  July 2007

We present a general theory for decomposing additive self-dual codes over $\mathbbF_4$ that have an automorphism of odd prime order. We apply the decomposition to codes of length $n$ with $13\leq n\leq30$ and automorphisms of prime order $r$ with $5\leq r\leq23$. Using this decomposition we classify all extremal/optimal additive self-dual codes with certain parameters in this list. In the process, we find the first $(18$, 218, $7)$, $(24$, 224, $8)$, and $(28$, 228, $10)$ Type I codes. We also improve the lower bounds on the number of known extremal/optimal additive self-dual codes for some values of $n$ with $13\leq n\leq 30$.
Keywords: self-dual codes, automorphisms., Additive codes over $\bbF_4$.
Mathematics Subject Classification: 94B1.
Citation: W. Cary Huffman. Additive self-dual codes over $\mathbb F_4$ with an automorphism of odd prime order. Advances in Mathematics of Communications, 2007, 1 (3) : 357-398. doi: 10.3934/amc.2007.1.357
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