Self-Dual Doubly Even 2-Quasi-Cyclic Transitive Codes Are Asymptotically Good

Authors:
C. Martinez-Perez;W. Willems
Affiliations:
Univ. de Zaragoza, Zaragoza;-
Venue:
IEEE Transactions on Information Theory
Year:
2007

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Abstract

In this correspondence, we prove that the class of binary self-dual doubly even 2-quasi-cyclic transitive codes is asymptotically good. This improves a recent result of Bazzi and Mitter (IEEE Trans. Inf. Theory, vol. 52, pp. 3210-3219, 2006). The proof is based on the study of a particular class of codes invariant under dihedral groups using a blend of representation theory and probabilistic arguments. The methods are closely related to those used in Bazzi and Mitter. In order to complete the proof a number theoretical result of Hasse is needed.