IEEE Access (Jan 2020)

On the Structure of Cyclic Codes Over <inline-formula> <tex-math notation="LaTeX">$\mathbb{F}_{q}{RS}$ </tex-math></inline-formula> and Applications in Quantum and LCD Codes Constructions

  • Hai Q. Dinh,
  • Tushar Bag,
  • Ashish Kumar Upadhyay,
  • Ramakrishna Bandi,
  • Warattaya Chinnakum

DOI
https://doi.org/10.1109/ACCESS.2020.2966542
Journal volume & issue
Vol. 8
pp. 18902 – 18914

Abstract

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Let p be an odd prime, q = pm, R = Fq + uFq with u2 = 1, and S = Fq + uFq + vFq + uvFq with u2 = 1, v2 = 1, uv = vu. In this paper, FqRS-cyclic codes over FqRS are studied. As an application, we present a construction of quantum error-correcting codes (QECCs) from the FqRS-cyclic codes over FqRS, which provides new QECCs. We also consider linear complementary dual (LCD) codes from the FqRS-cyclic codes over FqRS. Among others, we construct a Gray map over FqRS and discuss the Gray images of FqRS-cyclic codes over Fq.

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