American Institute of Mathematical Sciences

August  2008, 2(3): 309-343. doi: 10.3934/amc.2008.2.309

Additive cyclic codes over $\mathbb F_4$

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

Received  April 2008 Revised  July 2008 Published  July 2008

In this paper we find a canonical form decomposition for additive cyclic codes of even length over $\mathbb F_4$. This decomposition is used to count the number of such codes. We also prove that each code is the $\mathbb F_2$-span of at most two codewords and their cyclic shifts. We examine the construction of additive cyclic self-dual codes of even length and apply these results to those codes of length 24.
Citation: W. Cary Huffman. Additive cyclic codes over $\mathbb F_4$. Advances in Mathematics of Communications, 2008, 2 (3) : 309-343. doi: 10.3934/amc.2008.2.309
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