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arXiv · 2305.05157

A Generalized Covering Algorithm for Chained Codes

Ben Langton·Netanel Raviv
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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.

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Ben Langton, Netanel Raviv. 2023-05-09. A Generalized Covering Algorithm for Chained Codes. https://arxiv.org/abs/2305.05157

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