Year: 2022
Type: preprint
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 $m+2$ 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.
Source: arXiv (Cornell University)
Authors: Liu, Haibo, Liao, Qunying
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: 剩余码的设计及其相关的编码、译码问题研究
OpenAlex ID: W4226320677