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The study of ℤpℤp[u, v]-additive cyclic codes and their application in obtaining Optimal and MDSS codes Cover

The study of ℤpℤp[u, v]-additive cyclic codes and their application in obtaining Optimal and MDSS codes

Open Access
|May 2024

References

  1. Abualrub T and Siap I, Cyclic codes over the rings ℤ2 + u2 and ℤ2 + u2 + u22, Des. Codes Cryptogr. 42(2007) 273–287
  2. Abualrub T and Siap I, Reversible cyclic codes over ℤ4, Australas. J. Comb. 38(2007) 195–205.
  3. Abualrub T, Siap I and Aydin N, ℤ22-Additive cyclic codes, IEEE Trans. Inform. Theory 60(2014) 1508–1514
  4. Asamov T and Aydin N, Table of ℤ4 codes, Online available at http://www.asamov.com/4 Codes Accessed on 2019-12-12
  5. Ashraf M and Mohammad G, Skew cyclic codes over Fq + uFq + vFq, Asian-Eur. J. Math. 11(5)(2018)
  6. Aydogdu I, Abualrub T and Siap I, On ℤ22[u]-additive codes, Int. J. Comput. Math. 92(2015) 1806–1814
  7. Aydogdu I, Abualrub T and Siap I, The ℤ22[u]-cyclic and constacyclic codes, IEEE Trans. Inform. Theory 63(2017) 4883–4893
  8. I. Aydogdu, T. Abualrub and I. Siap, On the structure of ℤ22[u3]-linear and cyclic codes, Finite Fields Appl., 48(2017), 241–260.
  9. Aydogdu I and Siap I, The structure of ℤ22s -additive codes: Bounds on the minimum distance, Appl. Math. Inf. Sci. 7(2013) 2271–2278
  10. Aydogdu I and Siap I, On ℤprps-additive codes, Linear Multilinear Algebra 63(2015) 2089–2102
  11. Bierbrauer J, The theory of cyclic codes and a generalization to additive codes, Des. Codes Cryptogr 25(2002) 189–206
  12. Borges J, Fernandez-Cordoba C, Pujol J and Rifa J, ℤprps-additive cyclic codes, Adv. Math. Commun. 12(2018) 169–179
  13. Borges J, Fernandez-Cordoba C and Ten-Valls R, ℤ24-additive cyclic codes, generator polynomials and dual codes, IEEE Trans. Inform. Theory 62(2016) 6348–6354
  14. Calderbank A R and Sloane N J A, Modular and p-adic cyclic codes, Des. Codes Cryptogrph. 6(1995) 21–35
  15. Delsarte P, An Algebraic Approach to Association Schemes of Coding Theory, Philips Res. Rep., Supplement 1973
  16. Delsarte P and Levenshtein V I, Association schemes and coding theory, IEEE Trans. Inform. Theory 44(1998) 2477–2504
  17. Diao L and Gao J, ℤpp[v]-additive cyclic codes, Int. J. Comput. Math. 5(1)(2018) 1–17
  18. Islam H and Prakash O, On ℤpp[u, v]-additive cyclic and constacyclic codes, preprint (2019), arXiv:1905.06686v1.
  19. McDonald B R, Finite Rings with Identity (1974) Marcel Dekker Inc., New York
  20. MacWilliams F J and Sloane N J A, The Theory of Error-Correcting Codes(1977) North-Holland, Amsterdam
  21. Shi M, Wang C, Wu R, Hu Y and Chang Y, One-weight and two-weight ℤ22[u, v]-additive codes, Cryptogr. Commun. 12(2020) 443–454
  22. Yao T and Zhu S, ℤpps-additive cyclic codes are asymptotically good, Cryptogr. Commun. 12(2020) 253–264
DOI: https://doi.org/10.2478/auom-2024-0002 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 19 - 44
Submitted on: Jan 11, 2023
Accepted on: Apr 18, 2023
Published on: May 27, 2024
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2024 Mohammad Ashraf, Mohd Asim, Ghulam Mohammad, Washiqur Rehman, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.