Three new classes of optimal quinary cyclic codes with minimum distance four

Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an important subject of study for many years. Recently, several classes of optimal quinary cyclic codes of the forms C ( 0 , 1 , e ) and C ( 1 , e , s ) are presented in the...

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Published inApplicable algebra in engineering, communication and computing Vol. 36; no. 3; pp. 493 - 501
Main Authors Liu, Yan, Cao, Xiwang
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2025
Springer Nature B.V
Subjects
Artificial Intelligence
Codes
Communications systems
Computer Hardware
Computer Science
Data storage
Fields (mathematics)
Original Paper
Storage systems
Symbolic and Algebraic Manipulation
Theory of Computation
94B15
Quinary code
Minimum distance
Optimal code
Cyclic code
11T71
Online AccessGet full text
ISSN0938-1279
1432-0622
DOI10.1007/s00200-023-00621-7

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Summary:Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an important subject of study for many years. Recently, several classes of optimal quinary cyclic codes of the forms C ( 0 , 1 , e ) and C ( 1 , e , s ) are presented in the literature, where s = 5 m - 1 2 and 2 ≤ e ≤ 5 m - 2 . In this paper, by considering the solutions of certain equations over finite fields, we give three new classes of infinite families of optimal quinary cyclic codes of the form C ( 1 , e , s ) with parameters [ 5 m - 1 , 5 m - 2 m - 2 , 4 ] . Specifically, we make progress towards an open problem proposed by Gaofei Wu et al. [ 17 ].
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ISSN:0938-1279
1432-0622
DOI:10.1007/s00200-023-00621-7