Duality and LP Bounds for Codes with Locality
Information Theory
2022-12-16 v1 math.IT
Optimization and Control
Abstract
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.
Cite
@article{arxiv.2212.07805,
title = {Duality and LP Bounds for Codes with Locality},
author = {Anina Gruica and Benjamin Jany and Alberto Ravagnani},
journal= {arXiv preprint arXiv:2212.07805},
year = {2022}
}