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Some cyclic codes with prime length from cyclotomy of order 4

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Abstract

Cyclic codes are a subclass of linear codes and are widely used in many applications as they have efficient encoding and decoding algorithms. In this paper, we investigate two classes of cyclic codes over \(\mathbb {F}_{q}\) with prime length using cyclotomy of order 4. Both the dimensions and the generator polynomials are explicitly determined. The method serves as a connection between cyclic codes and sequences over \(\mathbb {F}_{q}\) whose supports are the unions of certain cyclotomic classes of order 4. The main results thus partially answer two open problems in Ding (2015).

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Acknowledgments

The author is grateful to the editor and two anonymous reviewers for careful reading and for many valuable comments that improved the quality of the paper. Q. Wang’s work was supported by the Shenzhen fundamental research programs under Grant no. JCYJ20150630145302234.

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  1. Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Xili Nanshan District, Shenzhen, Guangdong, 518055, China

    Qi Wang

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  1. Qi Wang
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Correspondence to Qi Wang.

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Wang, Q. Some cyclic codes with prime length from cyclotomy of order 4. Cryptogr. Commun. 9, 85–92 (2017). https://doi.org/10.1007/s12095-016-0188-3

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  • DOI: https://doi.org/10.1007/s12095-016-0188-3

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