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Symbol-pair weight distribution of some irreducible cyclic codes

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Abstract

In this paper, we study the symbol-pair weight distribution of some irreducible cyclic codes. We define generalized cyclotomic numbers and provide some of their properties. Using a character sum, we establish a relationship among the symbol-pair weight of irreducible cyclic codes, generalized cyclotomic numbers and the Gaussian periods. Moreover, we determine the symbol-pair weight distribution of some classes of irreducible cyclic codes.

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Acknowledgements

The authors are very grateful to the two anonymous reviewers and the editor for their detailed comments and suggestions that improved the quality of this paper. The authors are also grateful to Professor Ahmed Cherchem for helpful discussions.

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  1. Department of Mathematics, University of Sciences and Technology Houari Boumediene, Algiers, Algeria

    Youcef Maouche

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  1. Youcef Maouche
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Correspondence to Youcef Maouche.

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Maouche, Y. Symbol-pair weight distribution of some irreducible cyclic codes. Cryptogr. Commun. 15, 209–220 (2023). https://doi.org/10.1007/s12095-022-00599-y

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  • DOI: https://doi.org/10.1007/s12095-022-00599-y

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