A Generalized Covering Algorithm for Chained Codes
Abstract
The covering radius is a fundamental property of linear codes that characterizes the trade-off between storage and access in linear data-query protocols. The generalized covering radius was recently defined by Elimelech and Schwartz for applications in joint-recovery of linear data-queries. In this work we extend a known bound on the ordinary covering radius to the generalized one for all codes satisfying the chain condition -- a known condition which is satisfied by most known families of codes. Given a generator matrix of a special form, we also provide an algorithm which finds codewords which cover the input vectors within the distance specified by the bound. For the case of Reed-Muller codes we provide efficient construction of such generator matrices, therefore providing a faster alternative to a previous generalized covering algorithm for Reed-Muller codes.
Cite
@article{arxiv.2305.05157,
title = {A Generalized Covering Algorithm for Chained Codes},
author = {Ben Langton and Netanel Raviv},
journal= {arXiv preprint arXiv:2305.05157},
year = {2023}
}
Comments
8 pages, 9 figures. Conference paper accepted to 2023 IEEE International Symposium on Information Theory