LRCS: Duality, LP bounds, and field size
Abstract
We develop a duality theory of locally recoverable codes (LRCs) and apply it to establish a series of new bounds on their parameters. We introduce and study a refined notion of weight distribution that captures the code's locality. Using a duality result analogous to a MacWilliams identity, we then derive an LP-type bound that improves on the best known bounds in several instances. Using a dual distance bound and the theory of generalized weights, we obtain non-existence results for optimal LRCs over small fields. In particular, we show that an optimal LRC must have both minimum distance and block length relatively small compared to the field size.
Fields of Study & Subjects
Advanced Data Storage Technologies
Cellular Automata and Applications
Publication details
- Journal / source
- Designs Codes and Cryptography
- Publisher
- Springer Science and Business Media LLC
- Volume
- 94
- Issue
- 5
- Pages
- 100–100
- Publication date
- 25 April 2026
- Language
- EN