Linear Binary Codes Correcting One or More Errors
Information Theory
2025-12-16 v1 math.IT
Abstract
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal codeword length is derived. For the general case, a simple lower bound for the parameters of linear codes is derived from an analysis of the coset structure.
Cite
@article{arxiv.2512.12591,
title = {Linear Binary Codes Correcting One or More Errors},
author = {Timofei Izhitskii},
journal= {arXiv preprint arXiv:2512.12591},
year = {2025}
}