Abstract
Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their applications in cryptography, in the context of side channel and fault injection attacks. The security parameter for an LCP of codes (C, D) is defined as the minimum of the minimum distances d(C) and \(d(D^\bot )\). It has been recently shown that if C and D are both 2-sided group codes over a finite field, then C and \(D^\bot \) are permutation equivalent. Hence the security parameter for an LCP of 2-sided group codes (C, D) is simply d(C). We extend this result to 2-sided group codes over finite chain rings.
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Acknowledgements
We would like to thank the reviewers for their valuable comments, which drastically improved the manuscript. The first author is supported by the TÜBİTAK project 215E200, which is associated with the SECODE project in the scope of the CHIST-ERA Program. The second author is partially funded by the Spanish Research Agency (AEI) under Grant PGC2018-096446-B-C21. The third author visited the Institute of Mathematics of University of Valladolid during February–March 2019. She thanks the Institute for their kind hospitality.
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Communicated by J.-L. Kim.
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Güneri, C., Martínez-Moro, E. & Sayıcı, S. Linear complementary pair of group codes over finite chain rings. Des. Codes Cryptogr. 88, 2397–2405 (2020). https://doi.org/10.1007/s10623-020-00792-1
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DOI: https://doi.org/10.1007/s10623-020-00792-1