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Galois hulls of constacyclic codes over finite fields

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Abstract

This paper presents a formula for the dimension of Galois hulls of constacyclic codes. For this, we have arranged the irreducible factors of xn − λ over the finite field \(\mathbb {F}_{q}\) in a suitable way. Also, considering some restrictions on q, the number of constacyclic codes of length n over \(\mathbb {F}_{q}\) is calculated for a given Galois hull dimension.

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Acknowledgements

The authors would like to thank the CSIR, Govt. of India (under grant no. 09/1023(0030)/2019-EMR-I) and DST, Govt. of India (under CRG/2020/005927, vide Diary No. SERB/F/6780/ 2020-2021 dated 31 December, 2020) for providing financial support.

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  1. Department of Mathematics, Indian Institute of Technology Patna, Patna, 801 106, India

    Indibar Debnath, Om Prakash & Habibul Islam

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  1. Indibar Debnath
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Correspondence to Om Prakash.

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Debnath, I., Prakash, O. & Islam, H. Galois hulls of constacyclic codes over finite fields. Cryptogr. Commun. 15, 111–127 (2023). https://doi.org/10.1007/s12095-022-00591-6

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