# American Institute of Mathematical Sciences

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

 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 $13\leq n\leq 30$.
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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