A New Construction of Non-Binary Deletion Correcting Codes and their Decoding
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913975301570560 |
|---|---|
| author | Schaller, Michael Toesca, Beatrice Vu, Van Khu |
| author_facet | Schaller, Michael Toesca, Beatrice Vu, Van Khu |
| contents | Non-binary codes correcting multiple deletions have recently attracted a lot of attention. In this work, we focus on multiplicity-free codes, a family of non-binary codes where all symbols are distinct. Our main contribution is a new explicit construction of such codes, based on set and permutation codes. We show that our multiplicity-free codes can correct multiple deletions and provide a decoding algorithm. We also show that, for a certain regime of parameters, our constructed codes have size larger than all the previously known non-binary codes correcting multiple deletions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A New Construction of Non-Binary Deletion Correcting Codes and their Decoding Schaller, Michael Toesca, Beatrice Vu, Van Khu Information Theory Combinatorics Non-binary codes correcting multiple deletions have recently attracted a lot of attention. In this work, we focus on multiplicity-free codes, a family of non-binary codes where all symbols are distinct. Our main contribution is a new explicit construction of such codes, based on set and permutation codes. We show that our multiplicity-free codes can correct multiple deletions and provide a decoding algorithm. We also show that, for a certain regime of parameters, our constructed codes have size larger than all the previously known non-binary codes correcting multiple deletions. |
| title | A New Construction of Non-Binary Deletion Correcting Codes and their Decoding |
| topic | Information Theory Combinatorics |
| url | https://arxiv.org/abs/2501.13534 |