@inproceedings{e56a8249489f47c8a2205f62c901857a,
title = "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 vector(s) 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.",
keywords = "Covering codes, Reed-Muller codes",
author = "Ben Langton and Netanel Raviv",
note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 2023 IEEE International Symposium on Information Theory, ISIT 2023 ; Conference date: 25-06-2023 Through 30-06-2023",
year = "2023",
month = jan,
day = "1",
doi = "10.1109/ISIT54713.2023.10206543",
language = "English",
series = "IEEE International Symposium on Information Theory - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers",
pages = "844--849",
booktitle = "2023 IEEE International Symposium on Information Theory, ISIT 2023",
address = "United States",
}