Characterization of Nearly Self-Orthogonal Quasi-Twisted Codes and Related Quantum Codes

Abstract

Quasi-twisted codes are used here as the classical ingredients in the so-called Construction X for quantum error-control codes. The construction utilizes nearly self-orthogonal codes to design quantum stabilizer codes. We expand the choices of the inner product to also cover the symplectic and trace-symplectic inner products, in addition to the original Hermitian one. A refined lower bound on the minimum distance of the resulting quantum codes is established and illustrated. We report numerous record breaking quantum codes from our randomized search for inclusion in the updated online database.

arXiv comment18 pages, 8 tables; see also http://codetables.de This work has been submitted to the IEEE for possible publication; v2: corrected some typos, considerably expanded the tables with new quantum codes

References in corpus (8)

• Good Quantum Error-Correcting Codes Exist
• Multiple Particle Interference and Quantum Error Correction
• Quantum MDS Codes over Small Fields
• Quasi-Cyclic Constructions of Quantum Codes
• Good Stabilizer Codes from Quasi-Cyclic Codes over ${\mathbb{F}}_4$ and ${\mathbb{F}}_9$
• Algebraic Quantum Codes: Linking Quantum Mechanics and Discrete Mathematics
• On construction of quantum codes with dual-containing quasi-cyclic codes
• Equivalence of constacyclic codes with shift constants of different orders