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arXiv · 2607.03857

Function-Correcting Codes for Sum-Rank Metric

Santhi Kumari Kammila·B. Sundar Rajan
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Abstract

Function-Correcting Codes (FCCs) are a class of codes designed to protect the evaluation of a specific function of a message against channel errors at a higher level than the level of protection for the message, while requiring significantly less redundancy than conventional error-correcting codes. In this paper, we study function-correcting codes under the sum-rank metric, which is a natural generalization of both the Hamming metric and the rank-metric and also we derive general upper and lower bounds on the optimal redundancy of FCCs in the sum-rank metric. In particular, we establish a Plotkin-like bound for irregular-distance codes in sum-rank metric. Furthermore, we present explicit construction of function-correcting sum-rank metric codes (FCSRCs) for locally binary functions with optimal redundancy.

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Santhi Kumari Kammila, B. Sundar Rajan. 2026-07-04. Function-Correcting Codes for Sum-Rank Metric. https://arxiv.org/abs/2607.03857

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