Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 5 Sayı: 3, 143 - 151, 08.10.2018
https://doi.org/10.13069/jacodesmath.458601

Öz

Kaynakça

  • [1] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symb. Comput. 24(3–4) (1997) 235–265.
  • [2] I. Bouyukliev, "About the code equivalence" in Advances in Coding Theory and Cryptology, NJ, Hackensack: World Scientific, 2007.
  • [3] R. A. Brualdi, V. S. Pless, Weight enumerators of self–dual codes, IEEE Trans. Inform. Theory 37(4) (1991) 1222–1225.
  • [4] N. Chigira, M. Harada, M. Kitazume, Extremal self-dual codes of length 64 through neighbors and covering radii, Des. Codes Cryptogr. 42(1) (2007) 93–101.
  • [5] P. Çomak, J. L. Kim, F. Özbudak, New cubic self–dual codes of length 54; 60 and 66, Appl. Algebra Engrg. Comm. Comput. 29(4) (2018) 303–312.
  • [6] 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.
  • [7] S. T. Dougherty, T. A. Gulliver, M. Harada, Extremal binary self–dual codes, IEEE Trans. Inform. Theory 43(6) (1997) 2036–2047.
  • [8] M. Harada, T. Nishimura, R. Yorgova, New extremal self–dual codes of length 66, Math. Balkanica (N.S.) 21(1–2) (2007) 113–121.
  • [9] S. Karadeniz, B. Yildiz, New extremal binary self–dual codes of length 66 as extensions of self–dual codes over $R_k$, J. Franklin Inst. 350(8) (2013) 1963–1973.
  • [10] A. Kaya, New extremal binary self–dual codes of lengths 64 and 66 from $R_2$–lifts, Finite Fields Appl. 46 (2017) 271–279.
  • [11] A. Kaya, B. Yildiz, A. Pasa, New extremal binary self–dual codes from a modified four circulant construction, Discrete Math. 339(3) (2016) 1086–1094.
  • [12] A. Kaya, B. Yildiz, I. Siap, New extremal binary self–dual codes from F4 + uF4–lifts of quadratic circulant codes over F4, Finite Fields Appl. 35 (2015) 318–329.
  • [13] E. M. Rains, Shadow bounds for self–dual codes, IEEE Trans. Inform. Theory 44(1) (1998) 134–139.
  • [14] H.-P. Tsai, Existence of certain extremal self–dual codes, IEEE Trans. Inform. Theory 38(2) (1992) 501–504.
  • [15] H.-P. Tsai, Extremal self–dual codes of lengths 66 and 68, IEEE Trans. Inform. Theory 45(6) (1999) 2129–2133.
  • [16] N. Yankov, Self–dual [62; 31; 12] and [64; 32; 12] codes with an automorphism of order 7, Adv. Math. Commun. 8(1) (2014) 73–81.
  • [17] N. Yankov, M. H. Lee, M. Gürel, M. Ivanova, Self–dual codes with an automorphism of order 11, IEEE Trans. Inform. Theory 61(3) (2015) 1188–1193.
  • [18] N. Yankov, M. Ivanova, M. H. Lee, Self–dual codes with an automorphism of order 7 and s–extremal codes of length 68, Finite Fields Appl. 51 (2018) 17–30.

New extremal singly even self-dual codes of lengths 64 and 66

Yıl 2018, Cilt: 5 Sayı: 3, 143 - 151, 08.10.2018
https://doi.org/10.13069/jacodesmath.458601

Öz

For lengths $64$ and $66$,
we construct six and seven extremal singly even self-dual
codes with weight enumerators for which no extremal
singly even self-dual codes were previously known to exist, respectively.
We also construct new $40$ inequivalent
extremal doubly even self-dual $[64,32,12]$ codes
with covering radius $12$ meeting the Delsarte bound.
These new codes are constructed by considering
four-circulant codes along with their neighbors and shadows.

Kaynakça

  • [1] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symb. Comput. 24(3–4) (1997) 235–265.
  • [2] I. Bouyukliev, "About the code equivalence" in Advances in Coding Theory and Cryptology, NJ, Hackensack: World Scientific, 2007.
  • [3] R. A. Brualdi, V. S. Pless, Weight enumerators of self–dual codes, IEEE Trans. Inform. Theory 37(4) (1991) 1222–1225.
  • [4] N. Chigira, M. Harada, M. Kitazume, Extremal self-dual codes of length 64 through neighbors and covering radii, Des. Codes Cryptogr. 42(1) (2007) 93–101.
  • [5] P. Çomak, J. L. Kim, F. Özbudak, New cubic self–dual codes of length 54; 60 and 66, Appl. Algebra Engrg. Comm. Comput. 29(4) (2018) 303–312.
  • [6] 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.
  • [7] S. T. Dougherty, T. A. Gulliver, M. Harada, Extremal binary self–dual codes, IEEE Trans. Inform. Theory 43(6) (1997) 2036–2047.
  • [8] M. Harada, T. Nishimura, R. Yorgova, New extremal self–dual codes of length 66, Math. Balkanica (N.S.) 21(1–2) (2007) 113–121.
  • [9] S. Karadeniz, B. Yildiz, New extremal binary self–dual codes of length 66 as extensions of self–dual codes over $R_k$, J. Franklin Inst. 350(8) (2013) 1963–1973.
  • [10] A. Kaya, New extremal binary self–dual codes of lengths 64 and 66 from $R_2$–lifts, Finite Fields Appl. 46 (2017) 271–279.
  • [11] A. Kaya, B. Yildiz, A. Pasa, New extremal binary self–dual codes from a modified four circulant construction, Discrete Math. 339(3) (2016) 1086–1094.
  • [12] A. Kaya, B. Yildiz, I. Siap, New extremal binary self–dual codes from F4 + uF4–lifts of quadratic circulant codes over F4, Finite Fields Appl. 35 (2015) 318–329.
  • [13] E. M. Rains, Shadow bounds for self–dual codes, IEEE Trans. Inform. Theory 44(1) (1998) 134–139.
  • [14] H.-P. Tsai, Existence of certain extremal self–dual codes, IEEE Trans. Inform. Theory 38(2) (1992) 501–504.
  • [15] H.-P. Tsai, Extremal self–dual codes of lengths 66 and 68, IEEE Trans. Inform. Theory 45(6) (1999) 2129–2133.
  • [16] N. Yankov, Self–dual [62; 31; 12] and [64; 32; 12] codes with an automorphism of order 7, Adv. Math. Commun. 8(1) (2014) 73–81.
  • [17] N. Yankov, M. H. Lee, M. Gürel, M. Ivanova, Self–dual codes with an automorphism of order 11, IEEE Trans. Inform. Theory 61(3) (2015) 1188–1193.
  • [18] N. Yankov, M. Ivanova, M. H. Lee, Self–dual codes with an automorphism of order 7 and s–extremal codes of length 68, Finite Fields Appl. 51 (2018) 17–30.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Damyan Anev Bu kişi benim 0000-0002-3175-0168

Masaaki Harada Bu kişi benim 0000-0002-2748-6456

Nikolay Yankov Bu kişi benim 0000-0003-3703-5867

Yayımlanma Tarihi 8 Ekim 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 5 Sayı: 3

Kaynak Göster

APA Anev, D., Harada, M., & Yankov, N. (2018). New extremal singly even self-dual codes of lengths 64 and 66. Journal of Algebra Combinatorics Discrete Structures and Applications, 5(3), 143-151. https://doi.org/10.13069/jacodesmath.458601
AMA Anev D, Harada M, Yankov N. New extremal singly even self-dual codes of lengths 64 and 66. Journal of Algebra Combinatorics Discrete Structures and Applications. Ekim 2018;5(3):143-151. doi:10.13069/jacodesmath.458601
Chicago Anev, Damyan, Masaaki Harada, ve Nikolay Yankov. “New Extremal Singly Even Self-Dual Codes of Lengths 64 and 66”. Journal of Algebra Combinatorics Discrete Structures and Applications 5, sy. 3 (Ekim 2018): 143-51. https://doi.org/10.13069/jacodesmath.458601.
EndNote Anev D, Harada M, Yankov N (01 Ekim 2018) New extremal singly even self-dual codes of lengths 64 and 66. Journal of Algebra Combinatorics Discrete Structures and Applications 5 3 143–151.
IEEE D. Anev, M. Harada, ve N. Yankov, “New extremal singly even self-dual codes of lengths 64 and 66”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 5, sy. 3, ss. 143–151, 2018, doi: 10.13069/jacodesmath.458601.
ISNAD Anev, Damyan vd. “New Extremal Singly Even Self-Dual Codes of Lengths 64 and 66”. Journal of Algebra Combinatorics Discrete Structures and Applications 5/3 (Ekim 2018), 143-151. https://doi.org/10.13069/jacodesmath.458601.
JAMA Anev D, Harada M, Yankov N. New extremal singly even self-dual codes of lengths 64 and 66. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5:143–151.
MLA Anev, Damyan vd. “New Extremal Singly Even Self-Dual Codes of Lengths 64 and 66”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 5, sy. 3, 2018, ss. 143-51, doi:10.13069/jacodesmath.458601.
Vancouver Anev D, Harada M, Yankov N. New extremal singly even self-dual codes of lengths 64 and 66. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5(3):143-51.