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Quantum $(r,\delta)$-Locally Recoverable BCH and Homothetic-BCH Codes

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arxiv 2601.22567 v2 pith:IRMG4A5V submitted 2026-01-30 cs.IT math.ITquant-ph

Carlos Galindo , Fernando Hernando , Ryutaroh Matsumoto This is my paper · ORCID
classification cs.ITmath.ITquant-ph
keywords deltaquantumlrcscodeshomothetic-bchlocallyrecoverablearticle
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Quantum $(r,\delta)$-locally recoverable codes ($(r,\delta)$-LRCs) are the quantum version of classical $(r,\delta)$-LRCs designed to recover multiple failures in large-scale distributed and cloud storage systems. A quantum $(r,\delta)$-LRC, $Q(C)$, can be constructed from an $(r,\delta)$-LRC, $C$, which is Euclidean or Hermitian dual-containing. This article is devoted to studying how to get quantum $(r,\delta)$-LRCs from BCH and homothetic-BCH codes. As a consequence, we give pure quantum $(r,\delta)$-LRCs which are optimal for the Singleton-like bound.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Entanglement-Assisted Quantum Locally Recoverable Codes: Characterizations, Bounds, and Constructions

    cs.IT 2026-07 accept novelty 7.0 of 10

    First explicit optimal pure CSS-like EAQLRC families are constructed from ℓ-intersection MDS pairs and block parity-check matrices, with Singleton-like optimality and nontrivial locality.

  2. Information locality of a quantum locally recoverable code

    quant-ph 2026-08 accept novelty 6.0 of 10

    For quantum codes built from finite-field linear codes, a more accurate locality measure and an algorithm reduce the number of qudits and measurements needed for erasure repair.

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