Year: 2026
Type: preprint
Abstract: In this paper we derive new Delsarte-type linear programming bounds for $q$-ary $(r,δ)$-locally recoverable codes (LRCs) with three attributes: first, the variable set is comparable in size to that of the classical Delsarte LP; second, our LP exploits the higher-order information forced by the local-distance condition through order \(δ-2\), in the sense that for nondegenerate linear codes, its balanced base part gives exactly the same dimension bound as the symmetrized refined-weight LP of Gruica, Jany, and Ravagnani, while the additional constraints, nonvacuous whenever $δ\ge 3$, give a further strengthening; and third, it applies to general $(r,δ)$-LRCs, linear and nonlinear alike. Extensive computations over binary and ternary alphabets show that the convex-hull LP yields improvements not captured by the previous LP and often sharpens the shortening and generalized Singleton bounds.
Source: arXiv (Cornell University)
Authors: Li, Shujian, Wei, Hengjia, Xiong, Maosheng
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7201833489
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