Quantum MDS and synchronizable codes from cyclic codes of length 5ps over Fpm

Quantum MDS and synchronizable codes from cyclic codes of length 5ps over Fpm

For any odd prime p ≠ 5 , the structures of cyclic codes of length 5 p s over F p m are applied to construct quantum error-correcting codes (briefly, QEC codes). Some new QEC codes are provided in the sense that their parameters are different from all the previous constructions. We give all quantum...

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Bibliographic Details
Published in:Applicable algebra in engineering, communication and computing Vol. 34; no. 6; pp. 931 - 964
Main Authors: Dinh, Hai Q., Nguyen, Bac T., Tansuchat, Roengchai
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 2023
Springer Nature B.V
Subjects:
Artificial Intelligence
BCH codes
Computer Hardware
Computer Science
Error correcting codes
Error correction
Original Paper
Symbolic and Algebraic Manipulation
Theory of Computation
Primary 94B15
Hamming distance
Quantum synchronizable codes
Secondary 11T71
94B05
MDS codes
Quantum MDS codes
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Summary:For any odd prime p ≠ 5 , the structures of cyclic codes of length 5 p s over F p m are applied to construct quantum error-correcting codes (briefly, QEC codes). Some new QEC codes are provided in the sense that their parameters are different from all the previous constructions. We give all quantum maximum-distance-separable (briefly, qMDS codes) constructed by the CSS construction. We also construct quantum synchronizable codes (briefly, QSCs). To enrich the variety of available QSCs, many new QSCs are constructed to illustrate our results. Among them, there are QSCs codes with shorter lengths and much larger minimum distances than known primitive narrow-sense BCH codes.
ISSN:0938-1279
1432-0622
DOI:10.1007/s00200-021-00531-6