Self-Dual Doubly Even $2$-Quasi-Cyclic Transitive Codes Are Asymptotically Good
Conchita Martı́nez-Pérez, Wolfgang M. Willems · IEEE Transactions on Information Theory · 2007
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.