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

TL;DR

This article is devoted to studying how to get pure quantum $(r,\delta)$-LRCs from BCH and homothetic-BCH codes which are optimal for the Singleton-like bound.

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.

Theorems & Definitions (43)

• Definition 1
• Proposition 2
• Remark 3
• Definition 4
• Remark 5
• Theorem 6
• Remark 7
• Definition 8
• Proposition 9
• Theorem 10