A New Constructions of Minimal Binary Linear Codes
Information Theory
2022-01-11 v1 math.IT
Abstract
Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, secure two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then determining their weight distributions have been interesting in coding theory and cryptography. In this paper, a generic construction for binary linear codes with dimension is presented, then a necessary and sufficient condition for this binary linear code to be minimal is derived. Based on this condition and exponential sums, a new class of minimal binary linear codes violating the Ashikhmin-Barg condition is obtained, and then their weight enumerators are determined.
Cite
@article{arxiv.2201.02981,
title = {A New Constructions of Minimal Binary Linear Codes},
author = {Haibo Liu and Qunying Liao},
journal= {arXiv preprint arXiv:2201.02981},
year = {2022}
}