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

Authors: E. Bellini; M. Sala

Addresses: DarkMatter LLC, Abu Dhabi, 27655, UAE ' Department of Mathematics, University of Trento, Trento, TN, 38123, Italy

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.

Keywords: distance distribution; minimum distance; weight distribution; minimum weight; nonlinear code.

DOI: 10.1504/IJICOT.2018.091816

International Journal of Information and Coding Theory, 2018 Vol.5 No.1, pp.18 - 35

Received: 26 Jul 2017
Accepted: 31 Jul 2017
Published online: 18 May 2018 *