Araştırma Makalesi
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PERFECT CODES OVER HURWITZ INTEGERS INDUCED BY CIRCULANT GRAPHS

Yıl 2022, , 24 - 35, 01.03.2022
https://doi.org/10.33773/jum.985160

Öz

In this paper, a new family of t−error correcting perfect codes over Hurwitz integers is
presented. To obtain these perfect codes, the perfect t−dominating sets over the circulant
graphs are used. The codewords of such perfect codes are generated by the elements of a
subgroup of the considered group.

Proje Numarası

116F318

Kaynakça

  • [1] M. Güzeltepe, Codes over Hurwitz integers, Discrete Math. 313(2013), 704–714.
  • [2] M. Güzeltepe, A. Altınel, Perfect 1−error-correcting Hurwitz weight codes, Math. Commun. 22(2017), 265–272.
  • [3] M. Güzeltepe, O. Heden, Perfect Mannheim, Lipschitz and Hurwitz weight codes, Math. Commun. 19(2014), 253–276.
  • [4] R.W. Hamming, Error detecting and error correcting codes, Bell System Technical Journal 29(1950), 147—160.
  • [5] O. Heden, A new construction of group and nongroup perfect codes, Information and Control 34(1977), 314-–323.
  • [6] O. Heden, M. Güzeltepe, On perfect 1-ε-error-correcting codes, Math. Commun. 20(2015), 23—35.
  • [7] O. Heden, M. Güzeltepe, Perfect 1−error-correcting Lipschitz weight codes, Math. Commun. 21(2016), 23-–30.
  • [8] K. Huber, Codes over Gaussian integers, IEEE Trans. Inform. Theory 40(1994), 207—216.
  • [9] C.Y. Lee, Some properties of non-binary error correcting codes, IEEE Trans. Inform. Theory 4(1958), 77—82.
  • [10] B. B. Lindström , On group and nongroup perfect codes in q symbols, Math. Scand. 25(1969), 149-–158.
  • [11] C. Martínez, E. Stafford, R. Beivide, E. Gabidulin, Perfect codes over Lipschitz integers, in: Proc. IEEE Int. Symp. Information Theory, Nice, 2007, 1366— 1370.
  • [12] C. Martínez, R. Beivide, E. Gabidulin, Perfect codes from Cayley graphs over Lipschitz integers, IEEE Trans. Inf. Theory 55(2009), 3552-–3562.
  • [13] C. Martínez, R. Beivide, E. Gabidulin, Perfect codes for metrics induced by circulant graphs, IEEE Trans. Inf. Theory 53(2007), 3042—3052.
  • [14] J. Schönheim, On linear and nonlinear, single-error-correcting q−nary perfect codes, Information and Control 12(1968), 23-–26.
  • [15] Y.L. Vasil’ev, On nongroup close-packed codes, Problemi Tekhn. Kibernet. Robot. 8(1962), 337—339.
  • [16] J. G. Proakis, M. Salehi, Communications Systems Engineering, Second Edition, Prentice Hall.
  • [17] S. Lin, D. J. Costello, Jr., Error Control Coding, Second Edition, Prentice Hall.
Yıl 2022, , 24 - 35, 01.03.2022
https://doi.org/10.33773/jum.985160

Öz

Destekleyen Kurum

TÜBİTAK

Proje Numarası

116F318

Kaynakça

  • [1] M. Güzeltepe, Codes over Hurwitz integers, Discrete Math. 313(2013), 704–714.
  • [2] M. Güzeltepe, A. Altınel, Perfect 1−error-correcting Hurwitz weight codes, Math. Commun. 22(2017), 265–272.
  • [3] M. Güzeltepe, O. Heden, Perfect Mannheim, Lipschitz and Hurwitz weight codes, Math. Commun. 19(2014), 253–276.
  • [4] R.W. Hamming, Error detecting and error correcting codes, Bell System Technical Journal 29(1950), 147—160.
  • [5] O. Heden, A new construction of group and nongroup perfect codes, Information and Control 34(1977), 314-–323.
  • [6] O. Heden, M. Güzeltepe, On perfect 1-ε-error-correcting codes, Math. Commun. 20(2015), 23—35.
  • [7] O. Heden, M. Güzeltepe, Perfect 1−error-correcting Lipschitz weight codes, Math. Commun. 21(2016), 23-–30.
  • [8] K. Huber, Codes over Gaussian integers, IEEE Trans. Inform. Theory 40(1994), 207—216.
  • [9] C.Y. Lee, Some properties of non-binary error correcting codes, IEEE Trans. Inform. Theory 4(1958), 77—82.
  • [10] B. B. Lindström , On group and nongroup perfect codes in q symbols, Math. Scand. 25(1969), 149-–158.
  • [11] C. Martínez, E. Stafford, R. Beivide, E. Gabidulin, Perfect codes over Lipschitz integers, in: Proc. IEEE Int. Symp. Information Theory, Nice, 2007, 1366— 1370.
  • [12] C. Martínez, R. Beivide, E. Gabidulin, Perfect codes from Cayley graphs over Lipschitz integers, IEEE Trans. Inf. Theory 55(2009), 3552-–3562.
  • [13] C. Martínez, R. Beivide, E. Gabidulin, Perfect codes for metrics induced by circulant graphs, IEEE Trans. Inf. Theory 53(2007), 3042—3052.
  • [14] J. Schönheim, On linear and nonlinear, single-error-correcting q−nary perfect codes, Information and Control 12(1968), 23-–26.
  • [15] Y.L. Vasil’ev, On nongroup close-packed codes, Problemi Tekhn. Kibernet. Robot. 8(1962), 337—339.
  • [16] J. G. Proakis, M. Salehi, Communications Systems Engineering, Second Edition, Prentice Hall.
  • [17] S. Lin, D. J. Costello, Jr., Error Control Coding, Second Edition, Prentice Hall.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Murat Güzeltepe 0000-0002-2089-5660

Gökhan Güner Bu kişi benim 0000-0001-7634-3075

Proje Numarası 116F318
Yayımlanma Tarihi 1 Mart 2022
Gönderilme Tarihi 20 Ağustos 2021
Kabul Tarihi 1 Mart 2022
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Güzeltepe, M., & Güner, G. (2022). PERFECT CODES OVER HURWITZ INTEGERS INDUCED BY CIRCULANT GRAPHS. Journal of Universal Mathematics, 5(1), 24-35. https://doi.org/10.33773/jum.985160
AMA Güzeltepe M, Güner G. PERFECT CODES OVER HURWITZ INTEGERS INDUCED BY CIRCULANT GRAPHS. JUM. Mart 2022;5(1):24-35. doi:10.33773/jum.985160
Chicago Güzeltepe, Murat, ve Gökhan Güner. “PERFECT CODES OVER HURWITZ INTEGERS INDUCED BY CIRCULANT GRAPHS”. Journal of Universal Mathematics 5, sy. 1 (Mart 2022): 24-35. https://doi.org/10.33773/jum.985160.
EndNote Güzeltepe M, Güner G (01 Mart 2022) PERFECT CODES OVER HURWITZ INTEGERS INDUCED BY CIRCULANT GRAPHS. Journal of Universal Mathematics 5 1 24–35.
IEEE M. Güzeltepe ve G. Güner, “PERFECT CODES OVER HURWITZ INTEGERS INDUCED BY CIRCULANT GRAPHS”, JUM, c. 5, sy. 1, ss. 24–35, 2022, doi: 10.33773/jum.985160.
ISNAD Güzeltepe, Murat - Güner, Gökhan. “PERFECT CODES OVER HURWITZ INTEGERS INDUCED BY CIRCULANT GRAPHS”. Journal of Universal Mathematics 5/1 (Mart 2022), 24-35. https://doi.org/10.33773/jum.985160.
JAMA Güzeltepe M, Güner G. PERFECT CODES OVER HURWITZ INTEGERS INDUCED BY CIRCULANT GRAPHS. JUM. 2022;5:24–35.
MLA Güzeltepe, Murat ve Gökhan Güner. “PERFECT CODES OVER HURWITZ INTEGERS INDUCED BY CIRCULANT GRAPHS”. Journal of Universal Mathematics, c. 5, sy. 1, 2022, ss. 24-35, doi:10.33773/jum.985160.
Vancouver Güzeltepe M, Güner G. PERFECT CODES OVER HURWITZ INTEGERS INDUCED BY CIRCULANT GRAPHS. JUM. 2022;5(1):24-35.