Reductions Between Code Equivalence Problems
Computational Complexity
2025-11-27 v2
Abstract
In this paper we present two reductions between variants of the Code Equivalence problem. We give polynomial-time Karp reductions from Permutation Code Equivalence (PCE) to both Linear Code Equivalence (LCE) and Signed Permutation Code Equivalence (SPCE). Along with a Karp reduction from SPCE to the Lattice Isomorphism Problem (LIP) proved in a paper by Bennett and Win (2024), our second result implies a reduction from PCE to LIP.
Cite
@article{arxiv.2502.07916,
title = {Reductions Between Code Equivalence Problems},
author = {Mahdi Cheraghchi and Nikhil Shagrithaya and Alexandra Veliche},
journal= {arXiv preprint arXiv:2502.07916},
year = {2025}
}