发表机构
Indian Institute of Science, Bengaluru（印度科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对有限域上任意函数推导了Hamming度量下函数纠错码的广义Plotkin型冗余度界，并给出线性函数、Hamming权重函数及单项式映射的显式界。
AI 中文摘要
函数纠错码（FCCs）由Lenz等人（2023）近期提出，为接收端提供比消息保护级别更高的信道错误防护框架。本文针对有限域上任意函数，推导了Hamming度量下FCCs冗余度的广义Plotkin型界。所提出的界在经典纠错码情形下退化为经典Plotkin界。我们进一步获得了线性函数、Hamming权重函数和Hamming权重阈值函数的显式Plotkin型界。此外，我们研究了在编码理论、密码学和有限几何中广泛使用的单项式映射$f(x)=x^n$（$\nathbb{F}_{q^k}$上）的FCCs，并推导了显式的Plotkin型冗余度界。
英文摘要
Function-correcting codes, recently introduced by Lenz et al.\ (2023), provide a framework for the receiver to provide a higher level of protection against channel errors than the level of protection for messages. In this paper, we derive a generalised Plotkin-type bound on the redundancy of FCCs under the Hamming metric for arbitrary functions over finite fields. The proposed bound recovers the classical Plotkin bound for classical error-correcting codes as a special case. We further obtain explicit Plotkin-type bounds for linear functions, Hamming-weight functions, and Hamming-weight threshold functions. In addition, we study FCCs for monomial mappings $f(x)=x^n$ over $\mathbb{F}_{q^k}$, which are widely utilised in coding theory, cryptography, and finite geometry, and derive an explicit Plotkin-type redundancy bound.
CommentsProceedings of IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS), 2026 (To appear)
