The first tight classification of skew-constacyclic codes over finite fields

Monica Nevins; Susanne Pumluen

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arXiv · 2608.21339

The first tight classification of skew-constacyclic codes over finite fields

Monica Nevins·Susanne Pumluen

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Abstract

We parametrize the isometry and equivalence classes of skew constacyclic codes over a finite field by classifying the corresponding classes of their ambient rings, and present algorithms for the parametrizations. We achieve a tight classification by taking all possible Hamming-weight preserving isomorphisms between their ambient Petit rings into account. We also count the number of equivalence classes of these rings. We present many examples where isometry is a strictly stronger relation than equivalence, that is, codes that are isometric but not equivalent.

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Monica Nevins, Susanne Pumluen. 2026-08-21. The first tight classification of skew-constacyclic codes over finite fields. https://arxiv.org/abs/2608.21339

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