Related papers: Optimal Quantum $(r,δ)$-Locally Repairable Codes From Matrix-Product Codes

Optimal Quantum $(r,δ)$-Locally Repairable Codes From Matrix-Product Codes

URL: http://arxiv.org/abs/2508.03597v1
Date: Tue, 05 Aug 2025 16:05:14 GMT
Title: Optimal Quantum $(r,δ)$-Locally Repairable Codes From Matrix-Product Codes
Authors: Meng Cao, Kun Zhou,
Abstract summary: We study optimal quantum $(r,delta)$-LRCs from matrix-product (MP) codes.<n>We present five infinite families of optimal quantum $(r,delta)$-LRCs with flexible parameters.
Score: 52.3857155901121
License: http://creativecommons.org/licenses/by/4.0/
Abstract: This paper studies optimal quantum $(r,\delta)$-LRCs from matrix-product (MP) codes. We establish a necessary and sufficient condition for an MP code to be an optimal $(r,\delta)$-LRC. Based on this, we present a characterization for optimal quantum $(r,\delta)$-LRCs from MP codes with nested constituent codes, and also study optimal quantum $(r,\delta)$-LRCs constructed from MP codes with non-nested constituent codes. Through Hermitian dual-containing and Euclidean dual-containing MP codes, we present five infinite families of optimal quantum $(r,\delta)$-LRCs with flexible parameters.

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