AI 中文总结
本文针对线性码等价（LCE）和广义码等价（GCE）问题，提出了基于置换码等价搜索-决策归约的高效方法，可通过决策预言机及Engel-Schneider算法在确定性多项式时间内恢复相关分量。
AI 中文摘要
本文针对线性码等价（LCE）和广义码等价（GCE）问题提出了高效的搜索-决策归约方法，其思路源于近期针对置换码等价问题的搜索-决策归约研究。我们展示了如何利用决策预言机恢复等价关系中的置换分量，并借助用于对角等价的Engel-Schneider算法，给出了在确定性多项式时间内恢复对角分量与域自同构分量的方法。
英文摘要
In this paper, we present efficient search-to-decision reductions for the Linear Code Equivalence (LCE) and Generalised Code Equivalence (GCE) problems. Our methodology is inspired by the recent search-to-decision reduction for Permutation Code Equivalence. We demonstrate how to recover the permutation component of the equivalence using a decision oracle, and subsequently show one way of recovering the diagonal and field automorphism components in deterministic polynomial time by leveraging the elegant Engel-Schneider algorithm for diagonal equivalence.
