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A modified bordered construction for self-dual codes from group rings

Cilt: 7 Sayı: 2 7 Mayıs 2020
  • Joe Gıldea
  • Abidin Kaya
  • Alexander Tylyshchak
  • Bahattin Yıldız
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EN

A modified bordered construction for self-dual codes from group rings

Öz

We describe a bordered construction for self-dual codes coming from group rings. We apply the constructions coming from the cyclic and dihedral groups over several alphabets to obtain extremal binary self-dual codes of various lengths. In particular we find a new extremal binary self-dual code of length 78.

Anahtar Kelimeler

Kaynakça

  1. [1] D. Anev, N. Yankov, Self–dual codes of length 78 with an automorphism of order 13, in XVth International Workshop on Optimal Codes and Related Topics, Sofia, Bulgaria, July 2017.
  2. [2] F. Bernhardt, P. Landrock, O. Manz, The extended Golay codes considered as ideals, J. Combin. Theory Ser. A 55(2) (1990) 235–246.
  3. [3] J. H. Conway, N. J. A. Sloane, A new upper bound on the minimal distance of self–dual codes, IEEE Trans. Inform. Theory 36(6) (1990) 1319–1333.
  4. [4] R. Dontcheva, New binary [70; 35; 12] self-dual and binary [72; 36; 12] self-dual doubly-even codes, Serdica Mathematical Journal 24(4) (2001) 287–302.
  5. [5] S. T. Dougherty, J. Gildea, R. Taylor, A. Tylshchak, Group rings, G-Codes and constructions of self-dual and formally self-dual codes, Des. Codes Crypt. 86(9) (2018) 2115–2138.
  6. [6] S. T. Dougherty, P. Gaborit, M. Harada, P. Sole, Type II codes over $\mathbb{F}_{2}+u\mathbb{F}_{2}$, IEEE Trans. Inform. Theory 45 (1999) 32–45.
  7. [7] S. T. Dougherty, M. Harda, T. A. Gulliver, Extremal binary self-dual codes, IEEE Trans. Inform. Theory 43(6) (1997) 2036–2047.
  8. [8] S. T. Dougherty, B. Yildiz, S. Karadeniz, Codes over $R_k$, Gray maps and their binary images, Finite Fields Appl. 17(3) (2011) 205–219.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Mühendislik

Bölüm

Araştırma Makalesi

Yazarlar

Joe Gıldea Bu kişi benim
United Kingdom

Alexander Tylyshchak Bu kişi benim
Ukraine

Bahattin Yıldız Bu kişi benim
0000-0001-8106-3123
United States

Yayımlanma Tarihi

7 Mayıs 2020

Gönderilme Tarihi

19 Şubat 2019

Kabul Tarihi

22 Eylül 2019

Yayımlandığı Sayı

Yıl 2020 Cilt: 7 Sayı: 2

Kaynak Göster

APA
Gıldea, J., Kaya, A., Tylyshchak, A., & Yıldız, B. (2020). A modified bordered construction for self-dual codes from group rings. Journal of Algebra Combinatorics Discrete Structures and Applications, 7(2), 103-119. https://doi.org/10.13069/jacodesmath.729402
AMA
1.Gıldea J, Kaya A, Tylyshchak A, Yıldız B. A modified bordered construction for self-dual codes from group rings. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020;7(2):103-119. doi:10.13069/jacodesmath.729402
Chicago
Gıldea, Joe, Abidin Kaya, Alexander Tylyshchak, ve Bahattin Yıldız. 2020. “A modified bordered construction for self-dual codes from group rings”. Journal of Algebra Combinatorics Discrete Structures and Applications 7 (2): 103-19. https://doi.org/10.13069/jacodesmath.729402.
EndNote
Gıldea J, Kaya A, Tylyshchak A, Yıldız B (01 Mayıs 2020) A modified bordered construction for self-dual codes from group rings. Journal of Algebra Combinatorics Discrete Structures and Applications 7 2 103–119.
IEEE
[1]J. Gıldea, A. Kaya, A. Tylyshchak, ve B. Yıldız, “A modified bordered construction for self-dual codes from group rings”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 7, sy 2, ss. 103–119, May. 2020, doi: 10.13069/jacodesmath.729402.
ISNAD
Gıldea, Joe - Kaya, Abidin - Tylyshchak, Alexander - Yıldız, Bahattin. “A modified bordered construction for self-dual codes from group rings”. Journal of Algebra Combinatorics Discrete Structures and Applications 7/2 (01 Mayıs 2020): 103-119. https://doi.org/10.13069/jacodesmath.729402.
JAMA
1.Gıldea J, Kaya A, Tylyshchak A, Yıldız B. A modified bordered construction for self-dual codes from group rings. Journal of Algebra Combinatorics Discrete Structures and Applications. 2020;7:103–119.
MLA
Gıldea, Joe, vd. “A modified bordered construction for self-dual codes from group rings”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 7, sy 2, Mayıs 2020, ss. 103-19, doi:10.13069/jacodesmath.729402.
Vancouver
1.Joe Gıldea, Abidin Kaya, Alexander Tylyshchak, Bahattin Yıldız. A modified bordered construction for self-dual codes from group rings. Journal of Algebra Combinatorics Discrete Structures and Applications. 01 Mayıs 2020;7(2):103-19. doi:10.13069/jacodesmath.729402

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