Work

Plotkin-Like Bound and Explicit Function-Correcting Code Constructions for Lee Metric Channels

Year: 2026

Type: article

Abstract: Function-Correcting Codes (FCCs) are a novel class of codes designed to protect function evaluations of messages against errors while minimizing redundancy. A theoretical framework for systematic FCCs to channels matched to the Lee metric has been studied recently, which introduced function-correcting Lee distance codes (FCLCs) and also derived upper and lower bounds on their optimal redundancy. In this paper, we first propose a Plotkin-like bound for irregular Lee-distance codes. We then construct explicit FCLCs for specific classes of functions, including the Lee weight, Lee weight distribution, modular sum and locally bounded function. For these functions, lower bounds on redundancy are obtained, and our constructions are shown to be optimal in certain cases. Finally, a comparative analysis with classical Lee error-correcting codes and codes correcting errors in function values demonstrates that FCLCs can significantly reduce redundancy while preserving function correctness.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2026.3697793

Authors: K. Hareesh, N. T. Rashid Ummer, B. Sundar Rajan

Institution: Indian Institute of Science Bangalore

Language: English

Topic: Coding theory and cryptography

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Department of Science and Technology, Ministry of Science and Technology, India, Science and Engineering Research Board, Science and Engineering Research Council

OpenAlex ID: W7162641547

FWCI: 19.89

Cites: 18

Cited by: 10

Related to: 10