On the Existence of Hermitian Self-Dual Extended Abelian Group Codes

Simple item page
dc.creatorDicuangco, Lilibeth
dc.creatorMoree, Pieter
dc.creatorSole, Patrick
dc.date2006-04-02
dc.date.accessioned2026-07-07T07:10:24Z
dc.date.available2026-07-07T07:10:24Z
dc.descriptionSplit group codes are a class of group algebra codes over an abelian group. They were introduced in 2000 by Ding, Kohel and Ling as a generalization of the cyclic duadic codes. For a prime power q and an abelian group G of order n such that n and q are coprime, consider the group algebra F_{q^2}[G^{*}] of F_{q^2} over the dual group G^{*} of G. We prove that every ideal code in F_{q^{2}}[G^{*}] whose extended code is Hermitian self-dual is a split group code. We characterize the orders of finite abelian groups G for which an ideal code of F_{q^2}[G^{*}] whose extension is Hermitian self-dual exists and derive asymptotic estimates for the number of non-isomorphic abelian groups with this property.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0604013
dc.identifierhttp://arxiv.org/abs/math/0604013
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111410
dc.subjectRings and Algebras
dc.subjectNumber Theory
dc.subject11N64; 94B05; 11N37
dc.titleOn the Existence of Hermitian Self-Dual Extended Abelian Group Codes
dc.typetext

Files

Collections

arXiv