Moment-based linear programming bounds for locally recoverable codes

Shujian Li; Hengjia Wei; Maosheng Xiong

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arXiv · 2608.05758

Moment-based linear programming bounds for locally recoverable codes

Shujian Li·Hengjia Wei·Maosheng Xiong

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Abstract

In this paper we derive new Delsarte-type linear programming bounds for $q$-ary $(r,\delta)$-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 $\delta-2$, 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 $\delta \ge 3$, give a further strengthening; and third, it applies to general $(r,\delta)$-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.

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Shujian Li, Hengjia Wei, Maosheng Xiong. 2026-08-06. Moment-based linear programming bounds for locally recoverable codes. https://arxiv.org/abs/2608.05758

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