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

Soumak Biswas () and Maheshanand Bhaintwal ()
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Soumak Biswas: Indian Institute of Technology Roorkee
Maheshanand Bhaintwal: Indian Institute of Technology Roorkee

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 2, 375-388

Abstract: 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 .

Keywords: Quasi-cyclic codes; Quantum codes; Cyclotomic coset; Defining set; 94B05; 94B15; 94B60 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00259-0

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