Function-Correcting Codes for Locally Bounded Functions
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_ | 1866917076405321728 |
|---|---|
| author | Rajput, Charul Rajan, B. Sundar Freij-Hollanti, Ragnar Hollanti, Camilla |
| author_facet | Rajput, Charul Rajan, B. Sundar Freij-Hollanti, Ragnar Hollanti, Camilla |
| contents | In this paper, we introduce a class of functions that assume only a limited number $λ$ of values within a given Hamming $ρ$-ball and call them locally $(ρ, λ)$-bounded functions. We develop function-correcting codes (FCCs) for a subclass of these functions and propose an upper bound on the redundancy of FCCs. The bound is based on the minimum length of an error-correcting code with a given number of codewords and a minimum distance. Furthermore, we provide a sufficient optimality condition for FCCs when $λ= 4$. We also demonstrate that any function can be represented as a locally $(ρ, λ)$-bounded function, illustrating this with a representation of Hamming weight distribution functions. Furthermore, we present another construction of function-correcting codes for Hamming weight distribution functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Function-Correcting Codes for Locally Bounded Functions Rajput, Charul Rajan, B. Sundar Freij-Hollanti, Ragnar Hollanti, Camilla Information Theory In this paper, we introduce a class of functions that assume only a limited number $λ$ of values within a given Hamming $ρ$-ball and call them locally $(ρ, λ)$-bounded functions. We develop function-correcting codes (FCCs) for a subclass of these functions and propose an upper bound on the redundancy of FCCs. The bound is based on the minimum length of an error-correcting code with a given number of codewords and a minimum distance. Furthermore, we provide a sufficient optimality condition for FCCs when $λ= 4$. We also demonstrate that any function can be represented as a locally $(ρ, λ)$-bounded function, illustrating this with a representation of Hamming weight distribution functions. Furthermore, we present another construction of function-correcting codes for Hamming weight distribution functions. |
| title | Function-Correcting Codes for Locally Bounded Functions |
| topic | Information Theory |
| url | https://arxiv.org/abs/2504.07804 |