AI 中文总结
研究和秩度量下的函数纠错码，推导其最优冗余的上下界，建立类似Plotkin界，给出局部二元函数的函数纠错和秩度量码的显式构造。
AI 中文摘要
函数纠错码（FCCs）旨在比消息保护级别更高的层面保护消息特定函数的评估免受信道错误影响，且冗余比传统纠错码少得多。本文研究和秩度量下的FCCs，推导其最优冗余的上下界，建立和秩度量下不规则距离码的类似Plotkin界，还给出局部二元函数的函数纠错和秩度量码（FCSRCs）的显式构造。
英文摘要
Function-Correcting Codes (FCCs) are a class of codes designed to protect the evaluation of a specific function of a message against channel errors at a higher level than the level of protection for the message, while requiring significantly less redundancy than conventional error-correcting codes. In this paper, we study function-correcting codes under the sum-rank metric, which is a natural generalization of both the Hamming metric and the rank-metric and also we derive general upper and lower bounds on the optimal redundancy of FCCs in the sum-rank metric. In particular, we establish a Plotkin-like bound for irregular-distance codes in sum-rank metric. Furthermore, we present explicit construction of function-correcting sum-rank metric codes (FCSRCs) for locally binary functions with optimal redundancy.
CommentsExtended version of the paper presented in IEEE ISIT 2026. The presentation of the proof of Theorem 4 improved
