dc.contributor.authorJitman, Somphong
dc.contributor.authorLing, San
dc.contributor.authorSolé, Patrick
dc.identifier.citationJitman, S., Ling, S., & Solé, P. (2014). Hermitian self-dual abelian codes. IEEE Transactions on information theory, 60(3), 1496-1507.en_US
dc.description.abstractHermitian self-dual abelian codes in a group ring Fq2 [G], where Fq2 is a finite field of order q2 and G is a finite abelian group, are studied. Using the well-known discrete Fourier transform decomposition for a semi-simple group ring, a characterization of Hermitian self-dual abelian codes in Fq2 [G] is given, together with an alternative proof of necessary and sufficient conditions for the existence of such a code in Fq2 [G], i.e., there exists a Hermitian self-dual abelian code in Fq2 [G] if and only if the order of G is even and q = 2l for some positive integer l. Later on, the study is further restricted to the case where F22l [G] is a principal ideal group ring, or equivalently, G = A Z2k with 2 - jAj. Based on the characterization obtained, the number of Hermitian self-dual abelian codes in F22l [A Z2k ] can be determined easily. When A is cyclic, this result answers an open problem of Jia et al. concerning Hermitian self-dual cyclic codes. In many cases, F22l [A Z2k ] contains a unique Hermitian self-dual abelian code. The criteria for such cases are determined in terms of l and the order of A. Finally, the distribution of finite abelian groups A such that a unique Hermitian self-dual abelian code exists in F22l [A Z2] is established, together with the distribution of odd integers m such that a unique Hermitian self-dual cyclic code of length 2m over F22l exists.en_US
dc.format.extent14 p.en_US
dc.relation.ispartofseriesIEEE transactions on information theoryen_US
dc.rights© 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: [http://dx.doi.org/10.1109/TIT.2013.2296495].en_US
dc.titleHermitian self-dual abelian codesen_US
dc.typeJournal Article
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.description.versionAccepted versionen_US

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