Araştırma Makalesi

Some new ternary linear codes

Cilt: 4 Sayı: 3 15 Eylül 2017
  • Rumen Daskalov
  • Plamen Hristov
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EN

Some new ternary linear codes

Öz

Let an $[n,k,d]_q$ code be a linear code of length $n$, dimension $k$ and minimum Hamming distance $d$ over $GF(q)$. One of the most important problems in coding theory is to construct codes with optimal minimum distances. In this paper 22 new ternary linear codes are presented. Two of them are optimal. All new codes improve the respective lower bounds in [11].

Anahtar Kelimeler

Kaynakça

  1. [1] N. Aydin, I. Siap, D. Ray-Chaudhuri, The structure of 1–generator quasi–twisted codes and new linear codes, Des. Codes Cryptogr. 24(3) (2001) 313–326.
  2. [2] A. E. Brouwer, Bounds on the Size of Linear Codes, in Handbook of Coding Theory, V.S. PLess, W.C. Huffman, R.A. Brualdi(eds), Elsevier Amsterdam, 1998.
  3. [3] E. Z. Chen, Database of quasi–twisted codes, available at http://www.tec.hkr.se/~chen/ research/ codes/searchqc2.htm
  4. [4] E. Z. Chen, A new iterative computer search algorithm for good quasi–twisted codes, Des. Codes Cryptogr. 76(2) (2015) 307–323.
  5. [5] E. Chen, N. Aydin, A database of linear codes over $F_{13}$ with minimum distance bounds and new quasi–twisted codes from a heuristic search algorithm, J. Algebra Comb. Discrete Appl. 2(1) (2015) 1–16.
  6. [6] E. Chen, N. Aydin, New quasi–twisted codes over $F_{11}$-minimum distance bounds and a new database, J. Inf. Optim. Sci. 36(1–2) (2015) 129–157.
  7. [7] R. N. Daskalov, T. A. Gulliver, New good quasi–cyclic ternary and quaternary linear codes, IEEE Trans. Inform. Theory 43(5) (1997) 1647–1650.
  8. [8] R. Daskalov, P. Hristov, New one–generator quasi–cyclic codes over GF(7), Problemi Peredachi Informatsii 38(1) (2002) 59–63. English translation: Probl. Inf. Transm. 38(1) (2002) 50–54.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Mühendislik

Bölüm

Araştırma Makalesi

Yayımlanma Tarihi

15 Eylül 2017

Gönderilme Tarihi

14 Mayıs 2016

Kabul Tarihi

22 Mayıs 2016

Yayımlandığı Sayı

Yıl 2017 Cilt: 4 Sayı: 3

Kaynak Göster

APA
Daskalov, R., & Hristov, P. (2017). Some new ternary linear codes. Journal of Algebra Combinatorics Discrete Structures and Applications, 4(3), 227-234. https://doi.org/10.13069/jacodesmath.327360
AMA
1.Daskalov R, Hristov P. Some new ternary linear codes. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4(3):227-234. doi:10.13069/jacodesmath.327360
Chicago
Daskalov, Rumen, ve Plamen Hristov. 2017. “Some new ternary linear codes”. Journal of Algebra Combinatorics Discrete Structures and Applications 4 (3): 227-34. https://doi.org/10.13069/jacodesmath.327360.
EndNote
Daskalov R, Hristov P (01 Eylül 2017) Some new ternary linear codes. Journal of Algebra Combinatorics Discrete Structures and Applications 4 3 227–234.
IEEE
[1]R. Daskalov ve P. Hristov, “Some new ternary linear codes”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy 3, ss. 227–234, Eyl. 2017, doi: 10.13069/jacodesmath.327360.
ISNAD
Daskalov, Rumen - Hristov, Plamen. “Some new ternary linear codes”. Journal of Algebra Combinatorics Discrete Structures and Applications 4/3 (01 Eylül 2017): 227-234. https://doi.org/10.13069/jacodesmath.327360.
JAMA
1.Daskalov R, Hristov P. Some new ternary linear codes. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4:227–234.
MLA
Daskalov, Rumen, ve Plamen Hristov. “Some new ternary linear codes”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy 3, Eylül 2017, ss. 227-34, doi:10.13069/jacodesmath.327360.
Vancouver
1.Rumen Daskalov, Plamen Hristov. Some new ternary linear codes. Journal of Algebra Combinatorics Discrete Structures and Applications. 01 Eylül 2017;4(3):227-34. doi:10.13069/jacodesmath.327360

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