One-generator quasi-cyclic codes and their dual codes

Kanat Abdukhalikov, Tushar Bag, Daniel Panario

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this article, we study 1-generator quasi-cyclic (QC) codes over fields. QC codes of index l can be viewed as linear codes of length l. We give a description of the dual codes of 1-generator QC codes of index 2. Moreover, we obtain examples of quantum error-correcting codes (QECCs) from this study. They have better parameters than those from the online database. We consider self orthogonality conditions on such codes. We also construct some self orthogonal best known linear codes (BKLCs) linear codes, and using them we compute quantum codes. Using our symplectic study of QC codes, we are presenting three quantum codes with record-breaking parameters which improve the current record.

Original languageEnglish
Article number113369
JournalDiscrete Mathematics
Volume346
Issue number6
DOIs
Publication statusPublished - Jun 2023

Keywords

  • Dual codes
  • Quantum error-correcting codes (QECCs)
  • Quasi cyclic (QC) codes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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