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Paper:

TR26-200 | 8th September 2026 18:18

Subspace-Design Codes from LCL Derandomization: A Short Note

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TR26-200
Authors: Fernando Granha Jeronimo, Nikhil Shagrithaya
Publication: 20th September 2026 17:49
Downloads: 85
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Abstract:

Local LCL properties [Levi, Mosheiff, and Shagrithaya (LMS), FOCS 2025] give a language to express a broad range of linear properties of codes. Subspace design [Guruswami and Xing, 2013] is an elegant property about the linear structure of codes, and it governs important code behavior. In this note, we show that the subspace design property can be phrased as an LCL property. This allows us to recover the recent Goyal, Guruswami, and Hsieh result of constant-alphabet subspace-design codes from the earlier LCL derandomization framework [Jeronimo--Shagrithaya (JS), STOC 2026], with the same coarse alphabet dependence.



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