No More Perfect Codes: Classification of Perfect Quantum Codes

2009/07/01 by Zhuo Li, Li, Zhuo, Lijuan Xing +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Physics (quant-ph) #cs.IT #math.IT #quant-ph

paper · pdf · doi:10.48550/arxiv.0907.0049

3 pages, no figure

arxiv created 2009/07/01 · arxiv updated 2009/12/01

Abstract

We solve the problem of the classification of perfect quantum codes. We prove that the only nontrivial perfect quantum codes are those with the parameters . There exist no other nontrivial perfect quantum codes.

Cited by

• Haar random codes attain the quantum Hamming bound, approximately

Related

• Two infinite families of nonadditive quantum error-correcting codes
• Generalized Perfect Codes for Symmetric Classical-Quantum Channels
• New Symmetric and Asymmetric Quantum Codes
• Quantum Block and Synchronizable Codes Derived from Certain Classes of Polynomials
• Pasting Quantum Codes