Advances in Mathematics of Communications (AMC)

Additive cyclic codes over $\mathbb F_4$

Pages: 309 - 343, Volume 2, Issue 3, August 2008      doi:10.3934/amc.2008.2.309

       Abstract        Full Text (423.9K)       Related Articles       

W. Cary Huffman - Department of Mathematics and Statistics, Loyola University, Chicago, IL 60626, United States (email)

Abstract: 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.

Keywords:  Cyclic codes, additive codes, self-orthogonal codes, self-dual codes.
Mathematics Subject Classification:  Primary: 94B15.

Received: April 2008;      Revised: July 2008;      Available Online: July 2008.