The Length of Functional Batch and PIR Codes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917349142036480 |
|---|---|
| author | Kilic, Altan B. Ravagnani, Alberto Salizzoni, Flavio |
| author_facet | Kilic, Altan B. Ravagnani, Alberto Salizzoni, Flavio |
| contents | We consider the problem of computing the minimum length of functional batch and PIR codes of fixed dimension and for a fixed list size, over an arbitrary finite field. We recover, generalize, and refine several results that were previously obtained for binary codes. We present new upper and lower bounds for the minimum length, and discuss the asymptotic behaviour of this parameter. We also compute its value for several parameter sets. The paper also offers insights into the "correct" list size to consider for the Functional Batch Conjecture over non-binary finite fields, and establishes various supporting results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02586 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Length of Functional Batch and PIR Codes Kilic, Altan B. Ravagnani, Alberto Salizzoni, Flavio Information Theory We consider the problem of computing the minimum length of functional batch and PIR codes of fixed dimension and for a fixed list size, over an arbitrary finite field. We recover, generalize, and refine several results that were previously obtained for binary codes. We present new upper and lower bounds for the minimum length, and discuss the asymptotic behaviour of this parameter. We also compute its value for several parameter sets. The paper also offers insights into the "correct" list size to consider for the Functional Batch Conjecture over non-binary finite fields, and establishes various supporting results. |
| title | The Length of Functional Batch and PIR Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2508.02586 |