One-generator quasi-cyclic codes and their dual codes

Kanat Abdukhalikov; Tushar Bag; Daniel Panario

doi:10.1016/j.disc.2023.113369

One-generator quasi-cyclic codes and their dual codes

Kanat Abdukhalikov, Tushar Bag, Daniel Panario

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (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 language	English
Article number	113369
Journal	Discrete Mathematics
Volume	346
Issue number	6
DOIs	https://doi.org/10.1016/j.disc.2023.113369
Publication status	Published - 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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10.1016/j.disc.2023.113369

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title = "One-generator quasi-cyclic codes and their dual codes",

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.",

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AU - Abdukhalikov, Kanat

AU - Bag, Tushar

AU - Panario, Daniel

PY - 2023/6

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N2 - 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.

AB - 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.

KW - Dual codes

KW - Quantum error-correcting codes (QECCs)

KW - Quasi cyclic (QC) codes

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One-generator quasi-cyclic codes and their dual codes

Abstract

Keywords

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