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Constacyclic codes, cocycles and a u+v|u-v construction

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1 Author(s)
Hughes, G. ; Dept. of Math., R. Melbourne Inst. of Technol., Vic., Australia

A connection between cohomology, cocycles and constacyclic codes is explored. It suggests an isomorphism between cyclic codes of length mn and a direct sum of m constacyclic codes of length n. The isomorphism is used (i) to study the discrete Fourier transforms and the decomposition of group ring codes; (ii) to give a u+v|u-v construction over GF(q) when q is odd. The u+v|u-v construction gives some of the best ternary cyclic codes and classes of “nearly MDS” cyclic codes of length 2q+2. The symmetry of the construction is used to give a new proof that there are no cyclic self-dual codes over GF(q), when q is odd

Published in:

Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 2 )