Fast Algorithms for the Computation of the Minimum Distance of a Random Linear Code

TL;DR

This paper introduces optimized algorithms, including parallel and vectorized versions, for efficiently computing the minimum distance of random linear codes over _2, significantly outperforming existing methods on modern hardware.

Contribution

The paper presents a new family of algorithms with parallel and vectorized implementations that improve the speed of minimum distance computation for random linear codes.

Findings

Algorithms outperform current implementations in speed.

Parallel and vectorized implementations enhance performance.

Significant improvements on modern architectures.

Abstract

The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present and evaluate a family of algorithms and implementations to compute the minimum distance of a random linear code over $\mathbb{F}_{2}$ that are faster than different current implementations. In addition to the basic sequential implementations, we present parallel and vectorized implementations that render high performances on modern architectures. The attained performance results show the benefits of the developed optimized algorithms, which obtain remarkable performance improvements compared with state-of-the-art implementations widely used nowadays.