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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)=xn over 𝔽qk, which are widely utilised in coding theory, cryptography, and finite geometry, and derive an explicit Plotkin-type redundancy bound.

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Cite

BibTeXRIS
BibTeX
@misc{jagatti2026plotkintype,
  title = {{Plotkin-type Bound on Function-Correcting Codes for Monomial Mappings}},
  author = {Kanchana Lokshmii Jagatti and B. Sundar Rajan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04546},
  eprint = {2610.04546},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04546},
}
RIS
TY  - UNPB
TI  - Plotkin-type Bound on Function-Correcting Codes for Monomial Mappings
AU  - Kanchana Lokshmii Jagatti
AU  - B. Sundar Rajan
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04546
UR  - https://arxiv.org/abs/2610.04546
AB  - 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 𝔽_q^k, which are widely utilised in coding theory, cryptography, and finite geometry, and derive an explicit Plotkin-type redundancy bound.
ER  -