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

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

2006-04-02

arxiv.org/abs/math/0604013v1

Mathematics

Rings and Algebras

20 pages

Scientific paper

Split 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.

Affiliated with

Also associated with

No associations

Rating

On the Existence of Hermitian Self-Dual Extended Abelian Group Codes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Existence of Hermitian Self-Dual Extended Abelian Group Codes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Existence of Hermitian Self-Dual Extended Abelian Group Codes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-173266