Quantum $(r,δ)$-Locally Recoverable BCH and Homothetic-BCH Codes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914293473083392 |
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| author | Galindo, Carlos Hernando, Fernando Matsumoto, Ryutaroh |
| author_facet | Galindo, Carlos Hernando, Fernando Matsumoto, Ryutaroh |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_22567 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum $(r,δ)$-Locally Recoverable BCH and Homothetic-BCH Codes Galindo, Carlos Hernando, Fernando Matsumoto, Ryutaroh Information Theory Quantum Physics 81P45, 94B65, 11T71 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. |
| title | Quantum $(r,δ)$-Locally Recoverable BCH and Homothetic-BCH Codes |
| topic | Information Theory Quantum Physics 81P45, 94B65, 11T71 |
| url | https://arxiv.org/abs/2601.22567 |