A new method to obtain self-orthogonal codes over finite field F2 is presented. Based on this method, we provide a construction for quantum error-correcting codes starting from cyclic codes over finite ring R = F2 + uF2. As an example, we present infinite families of quantum error-correcting codes which are derived from cyclic codes over the ring R = F2 + uF2.

International Journal of Quantum InformationSep 1, 200990 citations

Reports on Mathematical Physics

NEW QUANTUM CODES DERIVED FROM THE DIRECT PRODUCT OF RINGS, USING CYCLIC CODES OVER THE RING

Pooja Soni, Manju Pruthi, Arun Kumar Yadav

Published Apr 1, 2024• 0 citations

Publisher

DOI: 10.1016/s0034-4877(24)00027-2

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In this paper, we extend the results given in [3] to a nonchain ring

R_p={\mathbb{F}}_p+v{\mathbb{F}}_p+{\cdots}+v^{p-1}{\mathbb{F}}_p

, where

v^p=v

and p is a prime. We determine the structure of the cyclic codes of arbitrary length over the ring

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and study the structure of their duals. We classify cyclic codes containing their duals over

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by giving necessary and sufficient conditions. Further, by taking advantage of the Gray map

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{\mathbb{F}}_p

which are obtained from cyclic codes over

R_p

. Finally, we illustrate the results by giving some examples.