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Impure codes exceeding the pure bounds for quantum local recovery
Carlos Galindo, Fernando Hernando, Helena Martín-Cruz, Ryutaroh Matsumoto·April 4, 2026
cs.ITQuantum Physics
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Abstract
Literature provides several bounds for quantum local recovery, which essentially consider the number of message qudits, the distance, the length, and the locality of the involved codes. We give a family of $J$-affine variety codes that result in impure CSS codes. These quantum codes exceed several of the above mentioned bounds that apply to pure quantum locally recoverable codes. We also discuss a connection between bounds on quantum local recovery and on weight-constrained stabilizer codes.