Reductions Between Code Equivalence Problems

Mahdi Cheraghchi; Nikhil Shagrithaya; Alexandra Veliche

Paper 2025/208

Reductions Between Code Equivalence Problems

Mahdi Cheraghchi

, University of Michigan–Ann Arbor

Nikhil Shagrithaya, University of Michigan–Ann Arbor

Alexandra Veliche

, University of Michigan–Ann Arbor

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.

Note: removed superfluous lemma (previously Lemma 3.3), made minor stylistic changes

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: code equivalence lattice isomorphism computational complexity
Contact author(s): mahdich @ umich edu
nshagri @ umich edu
aveliche @ umich edu
History: 2025-11-25: revised; 2025-02-11: received; See all versions
Short URL: https://ia.cr/2025/208
License: CC BY

BibTeX

@misc{cryptoeprint:2025/208,
      author = {Mahdi Cheraghchi and Nikhil Shagrithaya and Alexandra Veliche},
      title = {Reductions Between Code Equivalence Problems},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/208},
      year = {2025},
      url = {https://eprint.iacr.org/2025/208}
}