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Linear codes associated to determinantal varieties in the space of hermitian matrices

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Abstract

We introduce a new class of linear codes over a finite field associated to determinantal varieties in the space of hermitian matrices and determine their length, dimension and minimum distance along with the weight spectrum.

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Acknowledgements

The authors are thankful to the Editor and the referees for their constructive and insightful comments which are helpful in improving this work.

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  1. Kanchan Singh, Ritesh Kumar Pathak and Sheo Kumar Singh have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Mahatma Gandhi Central University, Motihari, Bihar, 845401, India

    Kanchan Singh, Ritesh Kumar Pathak & Sheo Kumar Singh

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  1. Kanchan Singh
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  2. Ritesh Kumar Pathak
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  3. Sheo Kumar Singh
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Correspondence to Ritesh Kumar Pathak.

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Communicated by G. Lunardon.

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Singh, K., Pathak, R.K. & Singh, S.K. Linear codes associated to determinantal varieties in the space of hermitian matrices. Des. Codes Cryptogr. (2024). https://doi.org/10.1007/s10623-024-01360-7

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  • DOI: https://doi.org/10.1007/s10623-024-01360-7

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