TY - JOUR
T1 - One-generator quasi-cyclic codes and their dual codes
AU - Abdukhalikov, Kanat
AU - Bag, Tushar
AU - Panario, Daniel
N1 - Funding Information:
K. Abdukhalikov and T. Bag are supported by the UAEU Grant G00003491 ; D. Panario is partially funded by the Natural Science and Engineering Research Council of Canada , reference number RPGIN-2018-05328 .
Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2023/6
Y1 - 2023/6
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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U2 - 10.1016/j.disc.2023.113369
DO - 10.1016/j.disc.2023.113369
M3 - Article
AN - SCOPUS:85150793873
SN - 0012-365X
VL - 346
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 6
M1 - 113369
ER -