Skew-cyclic CSS code

Skew-cyclic CSS code[1,2]

Description

A member of a family of Galois-qudit CSS codes constructed from skew-cyclic classical codes over rings [2; Thm. 5.8]. See related study [3] that uses cyclic codes over rings.

Cousins

Skew-cyclic code— Skew-cyclic CSS codes are constructed from classical skew-cyclic codes over rings.
Quantum maximum-distance-separable (MDS) code— Some quantum MDS codes are constructed from cyclic and constacyclic codes using the Galois-qudit CSS construction [2].

Member of code lists

Primary Hierarchy

Quantum Domain

Galois-qudit Kingdom

Galois-qudit codeQECC Quantum

Galois-qudit USt code

Galois-qudit stabilizer codeStabilizer Hamiltonian-based QECC Quantum

True Galois-qudit stabilizer code

Galois-qudit CSS codeCSS Stabilizer Hamiltonian-based QECC Quantum

Parents

Galois-qudit CSS code

Skew-cyclic CSS code

References

[1]: M. Özen, N. Tuğba Özzaim, and H. İnce, “Skew quasi cyclic codes over 𝔽q + v𝔽q”, Journal of Algebra and Its Applications 18, 1950077 (2019) DOI
[2]: H. Q. Dinh, T. Bag, A. K. Upadhyay, R. Bandi, and R. Tansuchat, “A class of skew cyclic codes and application in quantum codes construction”, Discrete Mathematics 344, 112189 (2021) DOI
[3]: M. Ashraf and G. Mohammad, “Quantum codes over Fp from cyclic codes over Fp[u, v]/〈u2 − 1, v3 − v, uv − vu〉”, Cryptography and Communications 11, 325 (2018) DOI

Page edit log

Victor V. Albert (2021-12-16) — most recent
Nolan Coble (2021-12-03)

Cite as:

“Skew-cyclic CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/skew-cyclic_galois_css

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits_galois/stabilizer/css/skew-cyclic_galois_css.yml.