Good Stabilizer Codes from Quasi-Cyclic Codes over F-4 and F-9

Ezerman M. F., Ling S., Ozkaya B., Sole P.

IEEE International Symposium on Information Theory (ISIT), Paris, France, 7 - 12 July 2019, pp.2898-2902, (Full Text) identifier

  • Publication Type: Conference Paper / Full Text
  • City: Paris
  • Country: France
  • Page Numbers: pp.2898-2902
  • Keywords: Construction X, Hermitian hull, quantum stabilizer code, quasi-cyclic code
  • Middle East Technical University Affiliated: No

Abstract

We apply quantum Construction X on quasi-cyclic codes with large Hermitian hulls over F-4 and 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.