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
收藏
页码：347 / 352
页数：6
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