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A class of constacyclic BCH codes

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Abstract

Constacyclic codes are a subclass of linear codes and have been well studied. Constacyclic BCH codes are a family of constacyclic codes and contain BCH codes as a subclass. Compared with the in-depth study of BCH codes, there are relatively little study on constacyclic BCH codes. The objective of this paper is to determine the dimension and minimum distance of a class of q-ary constacyclic BCH codes of length \(\frac {q^{m}-1}{q-1}\) with designed distances \(\delta _{i}=q^{m-1}-\frac {q^{\lfloor \frac {m-3}2 \rfloor +i }-1}{q-1}\) for \(1\leq i\leq \min \limits \{\lceil \frac {m+1}2 \rceil -\lfloor \frac {m}{q+1} \rfloor , \lceil \frac {m-1}2 \rceil \}\). As will be seen, some of these codes are optimal.

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Acknowledgements

The authors are grateful to the anonymous reviewers for careful reading and for valuable suggestions. Thank the reviewer for generously sharing the Magma programs with us so that we can check the correctness of the results in the text.

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Correspondence to Liqi Wang.

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This research is supported by the National Natural Science Foundation of China (61772168, 61572168, 61802102), the Natural Science Foundation of Anhui Province (1708085QA01), the China Scholarship Council (201806695004) and the Fundamental Research Funds for the Central Universities of China (PA2019GDZC009).

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Sun, Z., Zhu, S. & Wang, L. A class of constacyclic BCH codes. Cryptogr. Commun. 12, 265–284 (2020). https://doi.org/10.1007/s12095-019-00401-6

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  • DOI: https://doi.org/10.1007/s12095-019-00401-6

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