𝔽_qℛ-skew cyclic codes and their application to quantum codes

05/17/2023

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by   Om Prakash, et al.

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Let p be a prime and 𝔽_q be the finite field of order q=p^m. In this paper, we study 𝔽_qℛ-skew cyclic codes where ℛ=𝔽_q+u𝔽_q with u^2=u. To characterize 𝔽_qℛ-skew cyclic codes, we first establish their algebraic structure and then discuss the dual-containing properties by considering a non-degenerate inner product. Further, we define a Gray map over 𝔽_qℛ and obtain their 𝔽_q-Gray images. As an application, we apply the CSS (Calderbank-Shor-Steane) construction on Gray images of dual containing 𝔽_qℛ-skew cyclic codes and obtain many quantum codes with better parameters than the best-known codes available in the literature.