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

• URL: http://arxiv.org/abs/2601.22567v1
• Date: Fri, 30 Jan 2026 05:08:59 GMT
• Title: Quantum $(r,δ)$-Locally Recoverable BCH and Homothetic-BCH Codes
• Abstract summary: A quantum $(r,)$-LRC, $Q(C)$, can be constructed from an $(r,)$-LRC, $C$, which is Euclidean or Hermitian dual-containing.<n>This article is devoted to studying how to get quantum $(r,)$-LRCs from BCH and homothetic-BCH codes.
• Score: 39.53007356735723
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum $(r,δ)$-locally recoverable codes ($(r,δ)$-LRCs) are the quantum version of classical $(r,δ)$-LRCs designed to recover multiple failures in large-scale distributed and cloud storage systems. A quantum $(r,δ)$-LRC, $Q(C)$, can be constructed from an $(r,δ)$-LRC, $C$, which is Euclidean or Hermitian dual-containing. This article is devoted to studying how to get quantum $(r,δ)$-LRCs from BCH and homothetic-BCH codes. As a consequence, we give pure quantum $(r,δ)$-LRCs which are optimal for the Singleton-like bound.

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