Upper bounds on the size of quantum codes

Alexei Ashikhmin, Simon Litsyn

Research output: Contribution to journalArticlepeer-review


This paper is concerned with bounds for quantum error-correcting codes. Using the quantum MacWilliams identities, we generalize the linear programming approach from classical coding theory to the quantum case. Using this approach, we obtain Singleton-type, Hamming-type, and the first linear-programming-type bounds for quantum codes. Using the special structure of linear quantum codes, we derive an upper bound that is better than both Hamming and the first linear programming bounds on some subinterval of rates.

Original languageEnglish
Pages (from-to)1206-1215
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - 1999
Externally publishedYes


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