Additive double polycyclic codes over Fp2 and their applications to quantum codes

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Sarı M.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, vol.69, pp.4045-4068, 2023 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 69
  • Publication Date: 2023
  • Doi Number: 10.1007/s12190-023-01915-2
  • Journal Name: JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.4045-4068
  • Open Archive Collection: AVESIS Open Access Collection
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we introduce additive double polycyclic codes over Fp2" role="presentation" >
 for any prime p. We study their algebraic structures and determine generator polynomials of these codes. We also give cardinality of them. Additionally, we establish that both Euclidean dual and Hermitian dual of an additive double polycyclic code over Fp2" role="presentation" >
 are also an additive double polycyclic code over Fp2" role="presentation" >
. As practical applications of these codes, we exhibit additive double polycyclic codes over F9" role="presentation" >
 which contain triple as many codewords as optimal linear codes of same length and minimum distance over F9" role="presentation" >
, and we derive optimal ternary linear codes and quantum codes from additive double polycyclic codes over F9" role="presentation" >
.