Title :
Self-Dual Doubly Even 2-Quasi-Cyclic Transitive Codes Are Asymptotically Good
Author :
Martínez-Pérez, Conchita ; Willems, Wolfgang
Author_Institution :
Univ. de Zaragoza, Zaragoza
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.
Keywords :
correspondence principle; dual codes; 2-quasi-cyclic transitive codes; binary self-dual doubly; representation theory; Algebra; Linear code; Poles and towers; Rain; Welding; $2$-quasi-cyclic codes; Asymptotically good codes; doubly even codes; self-dual codes; transitive codes;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2007.907500