The first tight classification of skew-constacyclic codes over finite fields
2026-08-21 • Information Theory
Information Theory
AI summaryⓘ
The authors studied special types of error-correcting codes called skew constacyclic codes over finite fields. They classified these codes by looking at the related mathematical structures called ambient rings and created algorithms to organize them. By considering all possible ways to preserve code properties, they made a very detailed classification and counted how many unique types exist. They also found examples where two codes are very similar (isometric) but not exactly the same in structure (not equivalent).
skew constacyclic codesfinite fieldambient ringPetit ringisometrycode equivalenceHamming weighterror-correcting codes
Authors
Monica Nevins, Susanne Pumluen
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.