A Note on Function Correcting Codes for b-Symbol Read Channels

Abstract

Function-Correcting Codes (FCCs) is a novel paradigm in Error Control Coding introduced by Lenz et. al. 2023 for the binary substitution channel \cite{FCC}. FCCs aim to protect the function evaluation of data against errors instead of the data itself, thereby relaxing the redundancy requirements of the code. Later R. Premlal et. al. \cite{LFCC} gave new bounds on the optimal redundancy of FCCs and also extensively studied FCCs for linear functions. The notion of FCCs has also been extended to different channels such as symbol-pair read channel over the binary field by Xia et. al. \cite{FCSPC} and b-symbol read channel over finite fields by A.Singh et. al. \cite{FCBSC} In this work, we study FCCs for linear functions for the b-symbol read channel. We provide the Plotkin-like bound on FCCs for b-symbol read channel which reduces to a Plotkin-like bound for FCCs for the symbol-pair read channel when $b$=2. FCCs reduce to classical Error Correcting Codes (ECCs) when the function is bijective. Analogous to this our bound reduces to the Plotkin-bound for classical ECCS for both the b-symbol and symbol-pair read channels \cite{Plotkin-b-symbol, Plotkin-symbol-pair} when we consider linear bijective functions.