Linear codes that meet their dual trivially are also known as linear complementary dual codes. Quasi-abelian complementary dual codes are characterized using a known decomposition of a semisimple group algebra. Consequently, enumeration of such codes are obtained. More explicit formulas are given for the number of quasi-abelian complementary dual codes of index 2 with respect to Euclidean and Hermitian inner products. A sequence of asymptotically good binary quasi-abelian complementary dual codes of index 3 is constructed from an existing sequence of asymptotically good binary self-dual quasi-abelian codes of index 2.
CITATION STYLE
Jitman, S., Palines, H. S., & dela Cruz, R. B. (2017). On quasi-abelian complementary dual codes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10495 LNCS, pp. 192–206). Springer Verlag. https://doi.org/10.1007/978-3-319-66278-7_16
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