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Journal of Applied Mathematics and Computing

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16-11-2021 | Original Research

Enumeration of \({\mathbb {Z}}_4\)-double cyclic codes

Authors: Tian Wu, Jian Gao

Published in: Journal of Applied Mathematics and Computing | Issue 5/2022

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Abstract

In this paper, we study enumeration formulas of \({\mathbb {Z}}_4\)-double cyclic codes. We give the enumerations of separable \({\mathbb {Z}}_4\)-double cyclic codes and a class of non-separable \({\mathbb {Z}}_4\)-double cyclic codes with the coprime block lengths.

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Borges, J., Fernández-Córdoba, C., Ten-Valls, R.: \({\mathbb{Z}}_2\)-double cyclic codes. Des. Codes Cryptogr. 86, 463–479 (2018)MathSciNetCrossRef

Diao, L., Gao, J., Lu, J.: Some results on \({\mathbb{Z}}_p{\mathbb{Z}}_p[v]\)-additive cyclic codes. Adv. Math. Commun. 14, 555–572 (2020)MathSciNetCrossRef

Gao, J., Shi, M., Wu, T., Fu, F.-W.: On double cyclic codes over \({\mathbb{Z}}_4\). Finite Fields Their Appl. 39, 233–250 (2016)MathSciNetCrossRef

Gao, J., Hou, X.: \({\mathbb{Z}}_4\)-double cyclic codes are asymptotically good. IEEE Commun. Lett. 24, 1593–1597 (2020)CrossRef

Hammons, A.R., Kumar, P.V., Calderbank, A.R., Sloane, N.J.A., Solé, P.: The \({\mathbb{Z}}_4\)-linearity of Kerdock, Preparata, Goethals, and related codes. IEEE Trans. Inf. Theory 40, 301–319 (1994)CrossRef

Hou, X., Gao, J.: \({\mathbb{Z}}_p{\mathbb{Z}}_p[v]\)-additive cyclic codes are asymptotically good. J. Appl. Math. Comput. 66, 871–884 (2021)MathSciNetCrossRef

Hou, X., Gao, J.: n-Dimension quasi-twisted codes of arbitrary length over finite fields. J. Appl. Math. Comput. (2021). https://doi.org/10.1007/s12190-021-01540-xCrossRefMATH

Meng, X., Gao, J.: Complete weight enumerator of torsion codes. Adv. Math. Commun. (2021). https://doi.org/10.3934/amc.2020124CrossRefMATH

Shi, M., Huang, D., Sok, L., Solé, P.: Double circulant LCD codes over \({\mathbb{Z}}_4\). Finite Fields Appl. 58, 133–144 (2019)MathSciNetCrossRef

10.

Shi, M., Wu, R., Krotov, D.: On \({\mathbb{Z}}_p{\mathbb{Z}}_{p^k}\)-additive codes and their duality. IEEE Trans. Inf. Theory 65, 3842–3847 (2018)

11.

Shi, M., Wang, C., Wu, R., Hu, Y., Chang, Y.: One weight and two weight \({\mathbb{Z}}_2{\mathbb{Z}}_2[u, v]\)-additive codes. Cryptogr. Commun. 12, 443–454 (2020)MathSciNetCrossRef

12.

Shi, M., Qian, L., Solé, P.: On self-dual negacirculant codes of index two and four. Des. Codes Cryptogr. 11, 2485–2494 (2018)MathSciNetCrossRef

13.

Shi, M., Ozbudak, F., Xu, L., Solé, P.: LCD codes from tridiagonal Toeplitz matrices. Finite Fields Appl. 75, 101892 (2021)MathSciNetCrossRef

14.

Shi, M., Wu, R., Liu, Y., Solé, P.: Two and three weight codes over \({\mathbb{F}}_p+u{\mathbb{F}}_p\). Cryptogr. Commun. 9, 637–646 (2017)MathSciNetCrossRef

15.

Shi, M., Zhu, S., Yang, S.: A class of optimal \(p\)-ary codes from one-weight codes over \({\mathbb{F}}_p[u]/\langle u^m\rangle \). J. Franklin Inst. 350, 929–937 (2013)MathSciNetCrossRef

16.

Wan, Z.-X.: Quartenary Codes. Pte. World Scientific Publishing Company, Ltd (1997)

Title: Enumeration of -double cyclic codes
Authors: Tian Wu
Jian Gao
Publication date: 16-11-2021
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 5/2022
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-021-01668-w

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