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Counting Free ℤ𝟐ℤ𝟒ℤ𝟖-Additive Codes

Yıl 2020, Cilt: 13 Sayı: ÖZEL SAYI I, 70 - 75, 28.02.2020

Basri Çalışkan

https://doi.org/10.18185/erzifbed.617007
https://izlik.org/JA96BP57KD

Öz

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.

Anahtar Kelimeler

Lineer code free code additive code Gaussian binomial coefficient

Proje Numarası

OKÜBAP-2019-PT3-006

Kaynakça

  • 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.

Serbest Z_2 Z_4 Z_8-Toplamsal Kodları Sayma

Yıl 2020, Cilt: 13 Sayı: ÖZEL SAYI I, 70 - 75, 28.02.2020

Basri Çalışkan

https://doi.org/10.18185/erzifbed.617007
https://izlik.org/JA96BP57KD

Öz

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.



Anahtar Kelimeler

Lineer kod serbest kod toplamsal kod Gauss binom katsayısı

Destekleyen Kurum

Osmaniye Korkut Ata Üniversitesi Bilimsel Araştırma Projeleri Birimi

Proje Numarası

OKÜBAP-2019-PT3-006

Kaynakça

  • 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.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Basri Çalışkan 0000-0003-0512-4208

Proje Numarası OKÜBAP-2019-PT3-006
Yayımlanma Tarihi 28 Şubat 2020
DOI https://doi.org/10.18185/erzifbed.617007
IZ https://izlik.org/JA96BP57KD
Yayımlandığı Sayı Yıl 2020 Cilt: 13 Sayı: ÖZEL SAYI I

Kaynak Göster

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

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