A Class of Constacyclic Codes from Group Algebras

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Köroğlu M. E., Siap I.

FILOMAT, vol.31, pp.2917-2923, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31
  • Publication Date: 2017
  • Doi Number: 10.2298/fil1710917k
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2917-2923
  • Keywords: group algebras, cyclic codes, constacyclic codes
  • Yıldız Technical University Affiliated: Yes

Abstract

Constacyclic codes are preferred in engineering applications due to their efficient encoding process via shift registers. The class of constacyclic codes contains cyclic and negacyclic codes. The relation and presentation of cyclic codes as group algebras has been considered. Here for the first time, we establish a relation between constacyclic codes and group algebras and study their algebraic structures. Further, we give a method for constructing constacyclic codes by using zero-divisors in group algebras. Some good parameters for constacyclic codes which are derived from the proposed construction are also listed. 

Constacyclic codes are preferred in engineering applications due to their efficient encoding process via shift registers. The class of constacyclic codes contains cyclic and negacyclic codes. The relation and presentation of cyclic codes as group algebras has been considered. Here for the first time, we establish a relation between constacyclic codes and group algebras and study their algebraic structures. Further, we give a method for constructing constacyclic codes by using zero-divisors in group algebras. Some good parameters for constacyclic codes which are derived from the proposed construction are also listed.