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 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.

翻译：函数纠错码（FCCs）是一类新型码字，旨在保护消息的函数评估免受错误影响，同时最小化冗余度。近期，针对匹配Lee度量的信道，已有研究建立了系统化FCCs的理论框架，引入了函数纠错Lee码（FCLCs），并推导了其最优冗余度的上下界。本文首先提出非正则Lee距离码的类Plotkin界；随后针对特定函数类别（包括Lee权重、Lee权重分布、模和及局部有界函数）构造显式FCLCs。针对这些函数，我们获得了冗余度的下界，并证明在特定情况下所构造的码字是最优的。最后，通过与经典Lee纠错码及函数值纠错码的对比分析表明，FCLCs能够在保持函数正确性的同时显著降低冗余度。