Research Article
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Serbest Z_2 Z_4 Z_8-Toplamsal Kodları Sayma

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 70 - 75, 28.02.2020

Basri Çalışkan

https://doi.org/10.18185/erzifbed.617007
Cited By: 3

Abstract

Bu
çalışmada, Zα_2× Zβ_4× Zθ_8 uzayındaki serbest Z_2 Z_4 Z_8-toplamsal kodların tanımı yapılmış ve
bu kodların sayısı için bir formül elde edilmiştir.



Keywords

Lineer kod serbest kod toplamsal kod Gauss binom katsayısı

Supporting Institution

Osmaniye Korkut Ata Üniversitesi Bilimsel Araştırma Projeleri Birimi

Project Number

OKÜBAP-2019-PT3-006

References

  • Aydoğdu, I. and Gürsoy, F. 2019. “Z_2 Z_4 Z_8-Cyclic Codes”, Journal of Applied Mathematics and Computing, 60(1-2), 327-341.
  • Aydoğdu, I. and Şiap, I. 2013. “Counting The Generator Matrices of Z_2 Z_8-Codes”, Mathematical Sciences And Applications E-Notes, 1 (2), 143-149.
  • Bhowmik, G. 1996. “Evaluation of the divisor function of matrices”, Acta Arithmetica, 74, 155-159.
  • Bilal, M., Borges, J., Dougherty, S.T. and Fernández-Córdoba, C. 2010. “Optimal codes over Z_2 ×Z_4”, VII Jornadas de Matemática Discreta y Algorítmica Castro Urdiales, Cantabria, 7–9 de julio de.
  • Bilal, M., Borges, J., Dougherty, S.T. and Fernández-Córdoba, C. 2011. “Maximum distance separable codes over Z_4 and Z_2 〖×Z〗_4”, Designs, Codes and Cryptography, 61, 31-40.
  • Çalışkan, B. and Balıkçı, K. 2019. “Counting Z_2 Z_4 Z_8-Additive Codes”, European Journal of Pure And Applied Mathematics, 12 (2), 668-679.
  • Delsarte, S. 1948. “Fonctions de Möbius Sur les Groups Abeliens Finis”, Annals of Math. 49(3), 600-609.
  • Delsarte, P. 1973. “An algebraic approach to the association schemes of coding theory”, Philips Res. Rep. Suppl., 10.
  • Djubjuk, P.E. 1948. “On the number of subgroups of a finite abelian group”, Izv. Akad. Nauk SSSR Ser. Mat. 12, 351-378.
  • Dougherty, S.T. and Saltürk, E. 2016. Counting Z_2 Z_4-Additive Codes. Noncommutative Rings and Their Applications, Contemporary Mathematics, 634, 137-147.
  • Dougherty, S.T. and Fernández-Córdoba, C. 2011. Codes over Z_2^k, Gray map and self-dual codes, Advances in Mathematics of Communications, 5, 571-588.
  • Fernández-Córdoba, C., Pujol, J. and Villanueva, M. 2010. Z_2 Z_4-linear codes : rank and kernel, Designs, Codes and Cryptography, 56, 43-59.
  • Park, Y.H. 2009. Modular independence and generator matrices for codes over Z_m, Designs, Codes and Cryptography, 50, 147-162.
  • Pujol, J. ve Rifa, J., Translation Invarriant Propelinear Codes, IEEE Trans. Inform. Theory, 43, 590-598, 1997.
  • Saltürk, E. 2013. Bulanık Alt Grupların ve Kodların Sayısı ile Bazı Uygulamaları, Yıldız Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Doktora Tezi, 115.Yeh, Y. 1948. On Prime Power Abelian Groups. Bull. AMS, 54, 323-327.

Counting Free ℤ𝟐ℤ𝟒ℤ𝟖-Additive Codes

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 70 - 75, 28.02.2020

Basri Çalışkan

https://doi.org/10.18185/erzifbed.617007
Cited By: 3

Abstract

In this study, free ℤ2ℤ4ℤ8-additive codes in the space of ℤ2𝛼×ℤ4𝛽×ℤ8𝜃 are defined and obtained a formula for the number of these codes.

Keywords

Lineer code free code additive code Gaussian binomial coefficient

Project Number

OKÜBAP-2019-PT3-006

References

  • Aydoğdu, I. and Gürsoy, F. 2019. “Z_2 Z_4 Z_8-Cyclic Codes”, Journal of Applied Mathematics and Computing, 60(1-2), 327-341.
  • Aydoğdu, I. and Şiap, I. 2013. “Counting The Generator Matrices of Z_2 Z_8-Codes”, Mathematical Sciences And Applications E-Notes, 1 (2), 143-149.
  • Bhowmik, G. 1996. “Evaluation of the divisor function of matrices”, Acta Arithmetica, 74, 155-159.
  • Bilal, M., Borges, J., Dougherty, S.T. and Fernández-Córdoba, C. 2010. “Optimal codes over Z_2 ×Z_4”, VII Jornadas de Matemática Discreta y Algorítmica Castro Urdiales, Cantabria, 7–9 de julio de.
  • Bilal, M., Borges, J., Dougherty, S.T. and Fernández-Córdoba, C. 2011. “Maximum distance separable codes over Z_4 and Z_2 〖×Z〗_4”, Designs, Codes and Cryptography, 61, 31-40.
  • Çalışkan, B. and Balıkçı, K. 2019. “Counting Z_2 Z_4 Z_8-Additive Codes”, European Journal of Pure And Applied Mathematics, 12 (2), 668-679.
  • Delsarte, S. 1948. “Fonctions de Möbius Sur les Groups Abeliens Finis”, Annals of Math. 49(3), 600-609.
  • Delsarte, P. 1973. “An algebraic approach to the association schemes of coding theory”, Philips Res. Rep. Suppl., 10.
  • Djubjuk, P.E. 1948. “On the number of subgroups of a finite abelian group”, Izv. Akad. Nauk SSSR Ser. Mat. 12, 351-378.
  • Dougherty, S.T. and Saltürk, E. 2016. Counting Z_2 Z_4-Additive Codes. Noncommutative Rings and Their Applications, Contemporary Mathematics, 634, 137-147.
  • Dougherty, S.T. and Fernández-Córdoba, C. 2011. Codes over Z_2^k, Gray map and self-dual codes, Advances in Mathematics of Communications, 5, 571-588.
  • Fernández-Córdoba, C., Pujol, J. and Villanueva, M. 2010. Z_2 Z_4-linear codes : rank and kernel, Designs, Codes and Cryptography, 56, 43-59.
  • Park, Y.H. 2009. Modular independence and generator matrices for codes over Z_m, Designs, Codes and Cryptography, 50, 147-162.
  • Pujol, J. ve Rifa, J., Translation Invarriant Propelinear Codes, IEEE Trans. Inform. Theory, 43, 590-598, 1997.
  • Saltürk, E. 2013. Bulanık Alt Grupların ve Kodların Sayısı ile Bazı Uygulamaları, Yıldız Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Doktora Tezi, 115.Yeh, Y. 1948. On Prime Power Abelian Groups. Bull. AMS, 54, 323-327.
There are 15 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Makaleler
Authors

Basri Çalışkan 0000-0003-0512-4208

Project Number OKÜBAP-2019-PT3-006
Publication Date February 28, 2020
Published in Issue Year 2020 Volume: 13 Issue: ÖZEL SAYI I

Cite

APA Çalışkan, B. (2020). Serbest Z_2 Z_4 Z_8-Toplamsal Kodları Sayma. Erzincan University Journal of Science and Technology, 13(ÖZEL SAYI I), 70-75. https://doi.org/10.18185/erzifbed.617007

Cited By

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Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi
https://doi.org/10.47495/okufbed.1005844
Z_8+uZ_8+vZ_8 Üzerinde Aykırı Devirli Kodlar İçin Bazı Sonuçlar
European Journal of Science and Technology
Basri ÇALIŞKAN
https://doi.org/10.31590/ejosat.1010014
Does SARS-CoV-2 Trigger Stress-Induced Autoimmunity by Molecular Mimicry? A Hypothesis
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Francesco Cappello
https://doi.org/10.3390/jcm9072038