A New Approach to Code Smoothing Bounds
Information Theory
2026-03-20 v1 Cryptography and Security
math.IT
Abstract
To analyze the security of code-based cryptosystems, the smoothing parameter, which is closely related to the total variation distance of codes, has been investigated. While previous studies have bounded this distance using the Fourier transform on locally compact abelian groups, we take an alternative approach based on random walks. In this paper, we derive an inequality for the total variation distance of random walks using equitable partitions, and we show that our proposed bound generalizes existing results for finite abelian groups.
Keywords
Cite
@article{arxiv.2603.18077,
title = {A New Approach to Code Smoothing Bounds},
author = {Tsuyoshi Miezaki and Yusaku Nishimura and Katsuyuki Takashima},
journal= {arXiv preprint arXiv:2603.18077},
year = {2026}
}