Good Stabilizer Codes from Quasi-Cyclic Codes over ${\mathbb{F}}_4$ and ${\mathbb{F}}_9$

Abstract

We apply quantum Construction X on quasi-cyclic codes with large Hermitian hulls over ${\mathbb{F}}_4$ and ${\mathbb{F}}_9$ to derive good qubit and qutrit stabilizer codes, respectively. In several occasions we obtain quantum codes with stricly improved parameters than the current record. In numerous other occasions we obtain quantum codes with best-known performance. For the qutrit ones we supply a systematic construction to fill some gaps in the literature.

arXiv commentAccepted ISIT 2019

References in corpus (2)

• Multiple Particle Interference and Quantum Error Correction
• Quasi-Cyclic Constructions of Quantum Codes

Cited by in corpus (5)

• How Much Entanglement Does a Quantum Code Need?
• Algebraic Quantum Codes: Linking Quantum Mechanics and Discrete Mathematics
• On construction of quantum codes with dual-containing quasi-cyclic codes
• New Binary Quantum Codes Constructed from Quasi-Cyclic Codes
• Characterization of Nearly Self-Orthogonal Quasi-Twisted Codes and Related Quantum Codes