On Function-Correcting Lee Metric Codes with Data Protection
Abstract
Function-correcting codes are designed to protect the function values of a prescribed function against errors. Every error-correcting code that provides data protection inherently offers some degree of protection for functions defined on the data. In this work, we introduce a class of codes over ℤm, termed function-correcting Lee metric codes with data protection (FCLMCs with data protection), which simultaneously provide error protection for both the data and the corresponding function values under the Lee metric. We consider codes that provide protection against a prescribed level of error for the function values that exceeds the level of protection guaranteed for the underlying data. We present a general construction of these codes and derive lower and upper bounds on the optimal redundancy, including a Plotkin-type lower bound. Furthermore, we derive explicit upper bounds on the redundancy of FCLMCs with data protection for several important classes of functions, including locally binary Lee functions, the Lee weight function, and the modular sum function. Finally, since the Lee metric coincides with the Hamming metric over ℤ2, all of our results remain valid over ℤ2 with respect to the Hamming metric.
Related
- Data Protection in Function-Correcting Symbol-Pair Codes: Redundancy Bounds and Protection Profiles
- Function-Correcting Codes With Data Protection
- Plotkin-Like Bound and Explicit Function-Correcting Code Constructions for Lee Metric Channels
- Binary Multiple-Node-Erasure-Correcting Codes over Complete Graphs: Constructions, q-Ary Metric Balls, and Duality
- On systematicity of linear function-correcting codes
BibTeX
@misc{verma2026functioncorrecting,
title = {{On Function-Correcting Lee Metric Codes with Data Protection}},
author = {Gyanendra K. Verma and Abhay Kumar Singh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12217},
eprint = {2610.12217},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12217},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On Function-Correcting Lee Metric Codes with Data Protection
AU - Gyanendra K. Verma
AU - Abhay Kumar Singh
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12217
UR - https://arxiv.org/abs/2610.12217
AB - Function-correcting codes are designed to protect the function values of a prescribed function against errors. Every error-correcting code that provides data protection inherently offers some degree of protection for functions defined on the data. In this work, we introduce a class of codes over ℤ_m, termed function-correcting Lee metric codes with data protection (FCLMCs with data protection), which simultaneously provide error protection for both the data and the corresponding function values under the Lee metric. We consider codes that provide protection against a prescribed level of error for the function values that exceeds the level of protection guaranteed for the underlying data. We present a general construction of these codes and derive lower and upper bounds on the optimal redundancy, including a Plotkin-type lower bound. Furthermore, we derive explicit upper bounds on the redundancy of FCLMCs with data protection for several important classes of functions, including locally binary Lee functions, the Lee weight function, and the modular sum function. Finally, since the Lee metric coincides with the Hamming metric over ℤ_2, all of our results remain valid over ℤ_2 with respect to the Hamming metric.
ER -