On Function-Correcting Lee Metric Codes with Data Protection
This study addresses the joint protection of data and function values under the Lee metric by proposing a framework of function-correcting codes with data protection. Methodologically, it integrates algebraic coding theory, Plotkin bound analysis, and combinatorial construction techniques to design an asymmetric error-correction mechanism that provides stronger protection for functions than for data. The main contributions include establishing theoretical lower and upper bounds on optimal redundancy, deriving explicit redundancy upper bounds for specific function classes, and demonstrating that the proposed framework naturally extends to the Hamming metric. Ultimately, this work achieves a unified coding scheme that simultaneously accommodates data and function error correction, thereby providing both a theoretical foundation and a constructive paradigm for asymmetric protection coding.