In this paper, we introduce a class of functions that assume only a limited number of values within a given Hamming -ball and call them locally (, ) -bounded functions. We develop function-correcting codes (FCCs) for these functions and propose an upper bound on the redundancy of FCCs. The bound is based on the minimum length of an error-correcting code with a given number of codewords and a minimum distance. Furthermore, we provide a sufficient optimality condition for FCCs when =4. We also demonstrate that any function can be represented as a locally (, ) -bounded function, illustrating this with a representation of Hamming weight distribution functions. Furthermore, we present another construction of function-correcting codes for Hamming weight distribution functions.
Rajput et al. (Thu,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: