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
• Authors: Carlos Galindo, Fernando Hernando, Ryutaroh Matsumoto,
• 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.

Related papers

• Spectral Gaps with Quantum Counting Queries and Oblivious State Preparation [47.600794349481966]
  In this work, we present a quantum algorithm which approximates values up to additive error $epsilonDelta_k$ using a logarithmic number of qubits.<n>A key technical step in the analysis is the preparation of a suitable random initial state, which ultimately allows us to efficiently count the number of eigenvalues that are smaller than a threshold.
  arXiv  Detail & Related papers  (2025-08-28T17:04:18Z)
• Optimal Quantum $(r,δ)$-Locally Repairable Codes From Matrix-Product Codes [52.3857155901121]
  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.
  arXiv  Detail & Related papers  (2025-08-05T16:05:14Z)
• Optimal Quantum $(r,δ)$-Locally Repairable Codes via Classical Ones [52.3857155901121]
  Local repairable codes (LRCs) play a crucial role in mitigating data loss in large-scale distributed and cloud storage systems.<n>This paper establishes a unified decomposition theorem for general optimal $(r,delta)$-LRCs.<n>We construct three infinite families of optimal quantum $(r,delta)$-LRCs with flexible parameters.
  arXiv  Detail & Related papers  (2025-07-24T08:21:20Z)
• Quantum $(r,δ)$-locally recoverable codes [37.306043163932905]
  We introduce the quantum counterpart of those codes by defining quantum $(r,delta)$-locally recoverable codes.<n>We show that there is an equivalence between the classical and quantum concepts of $(r,delta)$-local recoverability.
  arXiv  Detail & Related papers  (2024-12-21T11:45:32Z)
• Quantum encoder for fixed Hamming-weight subspaces [0.0]
  We present an exact $n$-qubit computational-basis amplitude encoder of real- or complex data vectors of $d=binomnk$valued into a subspace of fixed Hamming weight $k$.<n>We show how our encoder can improve the performance of variational quantum algorithms for problems that include particle-string symmetries.<n>Our results constitute a versatile framework for quantum data compression with various potential applications in fields such as quantum chemistry, quantum machine learning, and constrained $k$ optimizations.
  arXiv  Detail & Related papers  (2024-05-30T18:26:41Z)
• Gate Based Implementation of the Laplacian with BRGC Code for Universal Quantum Computers [0.0]
  We study the gate-based implementation of the binary reflected Gray code (BRGC) and binary code of the unitary time evolution operator due to the Laplacian discretized on a lattice with periodic boundary conditions. We present our algorithm for building the BRGC quantum circuit.
  arXiv  Detail & Related papers  (2022-07-24T03:15:25Z)
• Quantum Coupon Collector [62.58209964224025]
  We study how efficiently a $k$-element set $Ssubseteq[n]$ can be learned from a uniform superposition $|Srangle of its elements. We give tight bounds on the number of quantum samples needed for every $k$ and $n$, and we give efficient quantum learning algorithms.
  arXiv  Detail & Related papers  (2020-02-18T16:14:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.