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Title:
Code Equivalence in the Sum-Rank Metric: Hardness and Completeness
Authors: Giuseppe D'Alconzo
Abstract:In this work, we define and study equivalence problems for sum-rank codes, giving their formulation in terms of tensors. Moreover, we introduce the concept of generating tensors of a sum-rank code, a direct generalization of the generating matrix for a linear code endowed with the Hamming metric. In this way, we embrace well-known definitions and problems for Hamming and rank metric codes. Finally, we prove the TI-completeness of code equivalence for rank and sum-rank codes, and hence, in the future, these problems could be used in the design of post-quantum schemes.
ePrint: https://eprint.iacr.org/2022/968
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