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A new construction of quantum codes from quasi-cyclic codes over finite fields

Author

Listed:
  • Soumak Biswas

    (Indian Institute of Technology Roorkee)

  • Maheshanand Bhaintwal

    (Indian Institute of Technology Roorkee)

Abstract

In this paper we present a construction of quantum codes from 1-generator quasi-cyclic (QC) codes of index 2 over a finite field $$\mathbb {F}_q$$ F q . We have studied QC codes of index 2 as a special case of $$\mathbb {F}_q$$ F q -double cyclic codes. We have determined the structure of the duals of such QC codes and presented a necessary and sufficient condition for them to be self-orthogonal. A construction of 1-generator QC codes with good minimum distance is also presented. To obtain quantum codes from QC codes, we use the Calderbank-Shor-Steane (CSS) construction. Few examples have been given to demonstrate this construction. Also, we present two tables of quantum codes with good parameters obtained from QC codes over $$\mathbb {F}_q$$ F q .

Suggested Citation

  • Soumak Biswas & Maheshanand Bhaintwal, 2023. "A new construction of quantum codes from quasi-cyclic codes over finite fields," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 375-388, June.
    • Handle: RePEc:spr:indpam:v:54:y:2023:i:2:d:10.1007_s13226-022-00259-0
    DOI: 10.1007/s13226-022-00259-0
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