码的等价性与自同构问题
Code Equivalence and Automorphism Problems for Codes
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中文总结 AI 辅助
本文证明码等价性问题与码的置换自同构群的计算问题（基数、轨道划分、生成集）多项式等价，并给出确定性多项式时间归约，适用于任意线性码。
中文摘要 AI 辅助
我们研究了码等价性问题的复杂性，并证明它与码的几个计算自同构问题多项式等价。这些问题要求计算码的置换自同构群的基数（ACOUNT）、轨道划分（APART）和生成集（AGEN）。我们给出了置换码等价性（PCE）与这些问题之间的确定性多项式时间归约，包括从搜索PCE到AGEN的一次性归约，该归约仅需一次预言机调用。我们还给出了线性码等价性（LCE）与码的单式自同构群的类似问题之间的类似归约。我们的所有归约适用于任何线性码。
英文摘要
We study the complexity of the Code Equivalence problem and show that it is polynomially equivalent to several computational automorphism problems for codes. These problems ask for the cardinality (ACOUNT), an orbit partition (APART), and a generating set (AGEN) for the permutation automorphism group of a code. We present deterministic, polynomial-time reductions between Permutation Code Equivalence (PCE) and each of these problems, including a one-shot reduction from search-PCE to AGEN that makes a single oracle call. We present similar reductions between Linear Code Equivalence (LCE) and analogous problems for the monomial automorphism group of a code. All of our reductions work for any linear codes.
