Abstract
We prove that if two linear codes are equivalent then they are semi-linearly equivalent. We also prove that if two additive MDS codes over a field are equivalent then they are additively equivalent.
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Acknowledgements
We are grateful to the referees who provided us with feedback which was very helpful. We would also like to thank Sam Adriaensen for observing that the proof of Theorem 1 implies that any equivalence between linear codes (which have generator matrices with no columns of weight one) is given by a permutation of the coordinates and a semi-linear affine map.
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Communicated by T. Feng.
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Simeon Ball acknowledges the support of the Spanish Ministry of Science and Innovation Grants MTM2017-82166-P and PID2020-113082GB-I00 funded by MCIN/AEI/10.13039/501100011033.
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Ball, S., Dixon, J. The equivalence of linear codes implies semi-linear equivalence. Des. Codes Cryptogr. 90, 1557–1565 (2022). https://doi.org/10.1007/s10623-022-01055-x
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DOI: https://doi.org/10.1007/s10623-022-01055-x