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标题: "Search-to-Decision Reductions for the Linear and General Code Equivalence Problems"
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---

## Computer Science > Information Theory

**arXiv:2608.10967** (cs)

## Title:Search-to-Decision Reductions for the Linear and General Code Equivalence Problems

Authors:[Abhinaba Mazumder](https://arxiv.org/search/cs?searchtype=author&query=Mazumder,+A)

[View PDF](https://arxiv.org/pdf/2608.10967) [HTML (experimental)](https://arxiv.org/html/2608.10967v1)

> Abstract: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.

| Subjects: | Information Theory (cs.IT) |
| --- | --- |
| Cite as: | [arXiv:2608.10967](https://arxiv.org/abs/2608.10967) \[cs.IT\] |
|  | (or [arXiv:2608.10967v1](https://arxiv.org/abs/2608.10967v1) \[cs.IT\] for this version) |
|  | [https://doi.org/10.48550/arXiv.2608.10967](https://doi.org/10.48550/arXiv.2608.10967) Focus to learn more  arXiv-issued DOI via DataCite (pending registration) |

## Submission history

From: Abhinaba Mazumder \[[view email](https://arxiv.org/show-email/1529494b/2608.10967)\]  
**\[v1\]** Tue, 11 Aug 2026 14:29:38 UTC (23 KB)

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