有限域上斜常循环码的首个紧分类
The first tight classification of skew-constacyclic codes over finite fields
AI总结：
该研究对有限域上斜常循环码的等距与等价类进行参数化，通过环境Petit环的同构实现紧分类，计数等价类数量并给出等距强于等价的例子。
AI中文摘要：
我们通过对其环境环的对应类进行分类，参数化有限域上斜常循环码的等距类与等价类，并给出参数化算法。我们通过考虑其环境Petit环间所有保持汉明重量的同构，实现紧分类，还计数了这些环的等价类数量。我们给出诸多例子，其中等距是比等价更严格的关系，即存在等距但不等价的码。
英文摘要：
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.
