A deterministic algorithm for the distance and weight distribution of binary nonlinear codes. (2018)

• Record Type: Journal Article
• Authors: Bellini, E.; Sala, M.
• Is Part Of: International journal of information and coding theory. Volume 5:Number 1(2018)
• Page Start: 18
• Page End: 35
• Publication Date: 2018
• Subjects: distance distribution -- minimum distance -- weight distribution -- minimum weight -- nonlinear code; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

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.