Plotkin-type Bound on Function-Correcting Codes for Monomial Mappings

Kanchana Lokshmii Jagatti; B. Sundar Rajan

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arXiv · 2610.04546

Plotkin-type Bound on Function-Correcting Codes for Monomial Mappings

Kanchana Lokshmii Jagatti·B. Sundar Rajan

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Abstract

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.

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BibTeX RIS

Kanchana Lokshmii Jagatti, B. Sundar Rajan. 2026-10-03. Plotkin-type Bound on Function-Correcting Codes for Monomial Mappings. https://arxiv.org/abs/2610.04546

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