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arXiv · 1905.11326

Invariants and Inequivalence of Linear Rank-Metric Codes

Alessandro Neri·Sven Puchinger·Anna-Lena Horlemann-Trautmann
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Abstract

We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an invariant for the whole equivalence class of the code. These invariants give rise to an easily computable criterion to check if two codes are inequivalent. With this criterion we then derive bounds on the number of equivalence classes of classical and twisted Gabidulin codes.

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Alessandro Neri, Sven Puchinger, Anna-Lena Horlemann-Trautmann. 2019-05-27. Invariants and Inequivalence of Linear Rank-Metric Codes. https://arxiv.org/abs/1905.11326

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