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Self-Dual Abelian Codes in Some Nonprincipal Ideal Group Algebras
Joint Authors
Jitman, Somphong
Choosuwan, Parinyawat
Udomkavanich, Patanee
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-10-27
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
The main focus of this paper is the complete enumeration of self-dual abelian codes in nonprincipal ideal group algebras F2k[A×Z2×Z2s] with respect to both the Euclidean and Hermitian inner products, where k and s are positive integers and A is an abelian group of odd order.
Based on the well-known characterization of Euclidean and Hermitian self-dual abelian codes, we show that such enumeration can be obtained in terms of a suitable product of the number of cyclic codes, the number of Euclidean self-dual cyclic codes, and the number of Hermitian self-dual cyclic codes of length 2s over some Galois extensions of the ring F2k+uF2k, where u2=0.
Subsequently, general results on the characterization and enumeration of cyclic codes and self-dual codes of length ps over Fpk+uFpk are given.
Combining these results, the complete enumeration of self-dual abelian codes in F2k[A×Z2×Z2s] is therefore obtained.
American Psychological Association (APA)
Choosuwan, Parinyawat& Jitman, Somphong& Udomkavanich, Patanee. 2016. Self-Dual Abelian Codes in Some Nonprincipal Ideal Group Algebras. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1112795
Modern Language Association (MLA)
Choosuwan, Parinyawat…[et al.]. Self-Dual Abelian Codes in Some Nonprincipal Ideal Group Algebras. Mathematical Problems in Engineering No. 2016 (2016), pp.1-12.
https://search.emarefa.net/detail/BIM-1112795
American Medical Association (AMA)
Choosuwan, Parinyawat& Jitman, Somphong& Udomkavanich, Patanee. Self-Dual Abelian Codes in Some Nonprincipal Ideal Group Algebras. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1112795
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1112795