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On Cyclic and Abelian Codes

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2 Author(s)
Polcino Milies, C. ; Inst. de Mat. e Estatistica, Univ. de Sao Paulo, São Paulo, Brazil ; Diniz de Melo, F.

In this paper, the minimum weight and the dimension of all cyclic codes of length pn over a field Fq, are computed, when p is an odd prime and Fq a finite field with q̅ elements, assuming that Fq generates the group of invertible elements of Zpn. Furthermore, the minimum weight and dimension of codes which are sum of two minimal codes in Fq(Cp×Cp) are also computed. Finally, the efficiency of cyclic codes and noncyclic abelian codes of length p2 are compared.

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Information Theory, IEEE Transactions on  (Volume:59 ,  Issue: 11 )