Abstract
We obtain a bound on the minimum distance of additive cyclic codes via the number of rational points on certain algebraic curves over finite fields. This is an extension of the analogous bound in the case of classical cyclic codes. Our result is the only general bound on such codes aside from Bierbrauer’s BCH bound. We compare our bounds’ performance against the BCH bound for additive cyclic codes in a special case and provide examples where it yields better results.
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Acknowledgments
The first author was supported by TÜBİTAK Project 114F432. The third author was supported by TÜBİTAK BİDEB 2211 National Ph.D. Scholarship Programme. The authors thank Kamil Otal for his help with Magma computations. We also thank the Reviewers for useful suggestions that improved the manuscript. In particular, Remark 8 was written in response to a question by one of the reviewers.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.
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Güneri, C., Özbudak, F. & Özdemir, F. Hasse–Weil bound for additive cyclic codes. Des. Codes Cryptogr. 82, 249–263 (2017). https://doi.org/10.1007/s10623-016-0198-3
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DOI: https://doi.org/10.1007/s10623-016-0198-3