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Open Access Research Article

Constacyclic codes over the non-chain finite commutative ring ℤ4[u,v]/<u2 – u, v2, uv>

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pp. 1867–1885Vol. 27Issue 6September 2024DOI: 10.47974/JDMSC-1873 Crossmark XML
Received:
14 Feb 2023
Published Online:
16 Sep 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1873
Pages:
1867–1885

Abstract

This paper considers (1+2u) -constacyclic and (1+2u) -skew constacyclic codes over the ring R = Z4[u,v]/

Keywords

Subject Classifications

94B0594B1594B3594B60

References

[1] T. Abualrub, I. Siap, Reversible cyclic codes over ℤ4,  Australas. J. Comb. 38 (2007) 195-206.
[2] M. Ashraf, G. Mohammad, (1+u) -constacyclic codes over ℤ4 + u4,  arXiv:1504.03445v1 (2015).
[3] Database of ℤ4  codes [online], http:// ℤ4  Codes. (Accessed March 2, 2020).
[4] D. Boucher, P. Solé, F. Ulmer, Skew constacyclic codes over Galois rings, Adv. Math. Commun. 2(3) 273-292 (2008).
[5] Y. Cengellenmis, A. Dertli, N. Aydın, Some constacyclic codes over  ℤ4[u]/<u2>  new Gray maps, and new quaternary codes, Algebra Colloq. 25(3), 369-376 (2018).
[6] J. Gao, F. Ma, F. Fu, Skew constacyclic codes over the ring Fq + vFq,  Appl. Comput. Math. 6(3), 286-295 (2017).
[7] F. Gursoy, I. Siap, B. Yildiz, Construction of skew cyclic codes over  Fq + vFq,  Adv. Math. Commun. 8(3), 313-322 (2014).
[8] A. R. Hammons, Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane, P. Solé, The ℤ4-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory 40(2), 301-319 (1994).
[9] H. Islam, O. Prakash, Skew cyclic and skew (α1 + uα2 +vα3 + uvα4) -constacyclic codes over Fq + uFq + vFq + uvFq,  Int. J. Inf. Coding Theory 5(2), 101-116 (2018).
[10] H. Islam, O. Prakash, A class of constacyclic codes over the ring  ℤ4[u,v] / <u2, v2, uv – vu>  and their Gray images, Filomat 33(8), 2237-2248 (2019).
[11] H. Islam, T. Bag, O. Prakash, A class of constacyclic codes over  ℤ4[u]/<uk>,  J. Applied Math. Computing 60(1-2), 237-251 (2019).
[12] E. Martínez-Moro, S. Szabo, B. Yildiz, Linear codes over  ℤ4[x]/<x2 + 2x>,  Int. J. Inf. Coding Theory 3(1), 78-96 (2015).
[13] M. Özen, N. T. Özzaim, N. Aydin, Cyclic codes over ℤ4 + u4 + u24,  Turkish J. Math. 41(5), 1235-1247 (2017).
[14] M Özen, F. Z. Uzekmek, N. Aydin, N. T. Özzaim, Cyclic and some constacyclic codes over the ring ℤ4[u]/<u2 – 1>,  Finite Fields Appl. 45, 27-39 (2016).
[15] V. S. Pless, Z. Qian, Cyclic codes and quadratic residue codes over  ℤ4, IEEE Trans. Inform. Theory 42(5), 1594-1600 (1996).
[16] M. Shi, L. Qian, L. Sok, N. Aydin, P. Solé, On constacyclic codes over  ℤ4[u]/<u2 – 1> and their Gray images, Finite Fields Appl. 45, 86-95 (2017).
[17] I. Siap, T. Abualrub, N. Aydin, P. Seneviratne, Skew cyclic codes of arbitrary length, Int. J. Inf. Coding Theory 2, 10-20 (2011).
[18] T. Yao, M. Shi, P. Solé, On Skew cyclic codes over Fq + uFq + vFq + uvFq,   J. Algebra Comb. Discrete Struct. Appl. 2(3), 163-168 (2015).
[19] B. Yildiz, A. Kaya, Self-dual codes over ℤ4[x]/<x2 + 2x>  and the  ℤ4 -images, Int. J. Inf. Coding Theory 5(2), 142-154 (2018).
[20] B. Yildiz, N. Aydin, On cyclic codes over ℤ4 + uℤ4  and their ℤ4-image, Int. J. Inf. Coding Theory 2, 226-237 (2014).
[21] H. Yu, Y. Wang, M. Shi, (1 + u) -constacyclic codes over ℤ4 + uℤ4,  SpringerPlus 5, 1325 (2016).

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