A deterministic algorithm for the distance and weight distribution of binary nonlinear codes

TL;DR

This paper introduces a deterministic algorithm leveraging Fourier techniques to efficiently compute the weight and distance distribution of binary nonlinear codes, especially effective for codes with low information rate.

Contribution

The paper presents a novel deterministic algorithm that improves computation of weight and distance distributions for binary nonlinear codes, utilizing fast Fourier methods.

Findings

Algorithm performs comparably to best-known algorithms on average

Particularly efficient for codes with low information rate

Provides complexity estimates for various cases

Abstract

Given a binary nonlinear code, we provide a deterministic algorithm to compute its weight and distance distribution, and in particular its minimum weight and its minimum distance, which takes advantage of fast Fourier techniques. This algorithm's performance is similar to that of best-known algorithms for the average case, while it is especially efficient for codes with low information rate. We provide complexity estimates for several cases of interest.