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.
| Original language | English |
|---|---|
| Title of host publication | 2023 IEEE Information Theory Workshop, ITW 2023 |
| Publisher | IEEE/LEOS |
| Pages | 347-352 |
| Number of pages | 6 |
| ISBN (Electronic) | 9798350301496 |
| ISBN (Print) | 979-8-3503-0150-2 |
| DOIs | |
| Publication status | Published - 28 Apr 2023 |
| Event | 2023 IEEE Information Theory Workshop (ITW) - Saint-Malo, France Duration: 23 Apr 2023 → 28 Apr 2023 |
Conference
| Conference | 2023 IEEE Information Theory Workshop (ITW) |
|---|---|
| Period | 23/04/23 → 28/04/23 |
Keywords
- Codes
- Conferences
- locally recoverable code
- LP bound
- MacWilliams identities
- dual distance
- locality
- linear programming
- duality