Duality and LP Bounds for Codes with Locality

被引：0

作者：

Gruica, Anina ^{[1
]}

Jany, Benjamin ^{[2
]}

Ravagnani, Alberto ^{[1
]}

机构：

[1] Eindhoven Univ Technol, Dept Math & Comp Sci, Eindhoven, Netherlands

[2] Univ Kentucky, Dept Math, Lexington, KY USA

来源：

2023 IEEE INFORMATION THEORY WORKSHOP, ITW | 2023年

基金：

荷兰研究理事会;

关键词：

locality; locally recoverable code; duality; linear programming; LP bound; dual distance; MacWilliams identities; REPAIRABLE CODES; CONSTRUCTIONS;

D O I：

10.1109/ITW55543.2023.10161676

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We initiate the study of the duality theory of locally recoverable codes, with a focus on the applications. We characterize the locality of a code in terms of the dual code, and introduce a class of invariants that refine the classical weight distribution. In this context, we establish a duality theorem analogous to (but very different from) a MacWilliams identity. As an application of our results, we obtain two new bounds for the parameters of a locally recoverable code, including an LP bound that improves on the best available bounds in several instances.

引用

页码：347 / 352

页数：6

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