Öz
In this correspondence, we consider quadratic double and bordered double circulant construction methods over the ring R := F_2 + uF_2 + u^2F_2, where u^3 = 1. Among other examples, extremal binary self-dual codes of length 66 are obtained by these constructions. These are extended by using extension theorems for self-dual codes and as a result 8 new extremal binary self-dual codes of length 68 are obtained. More precisely, codes with beta=117, 120, 133 in W68;1 and with gamma = 1, beta=49, 57, 59 and codes with gamma=2, beta=69, 81 in W68;2 are constructed for the ?first time in the literature. In addition to these, some known such codes are reconstructed via this extension. The results are tabulated.
Anahtar Kelimeler
Extremal codes Codes over rings Gray maps Quadratic double-circulant codes
Kaynakça
- 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), 1319-1333, 1990.
- S. T. Dougherty, T. A. Gulliver, M., Harada, Extremal binary self dual codes, IEEE Trans. Inform. Theory, 43(6), 2036-2047, 1997.
- P. Gaborit, Quadratic double circulant codes over fields, Journal of Combinatorial Theory Series A, 97(1), 85-107, 2002.
- W.C. Huffman, V. Pless, Fundamentals of error correcting codes, Cambridge University press, 2003.
- J.-L. Kim, New extremal self-dual codes of lengths 36, 38 and 58, IEEE Trans. Inf. Theory, 47(1), 386-393, 2001.
- A. Kaya, B. Yildiz, İ. Şiap, New extremal binary self-dual codes from F4+ uF4-lifts of quadratic double circulant codes over F, available online at http://arxiv.org/abs/1405.7147
- A. Kaya, B. Yildiz, Binary generator matrices of new extremal self-dual binary codes of length 68, available online at http://www.fatih.edu.tr/~akaya/binary/68u31.txt
- A. Kaya, B. Yildiz, Extension theorems for self-dual codes over rings and new binary self-dual codes, available online at http://arxiv.org/abs/1404.0195.
- E. M. Rains, Shadow Bounds for Self Dual Codes, IEEE Trans. Inf. Theory, 44(1), 134-139, 1998.
- H.-P. Tsai, P.-Y. Shih, R.-Y. Wuh, W.-K. Su, C.-H. Chen, Construction of self-dual codes, IEEE
- Trans. Inform. Theory, 54(8), 3826-3831, 2008.
Öz
In this correspondence, we consider quadratic double and bordered double circulant construction methods over the ring R := F_2 + uF_2 + u^2F_2, where u^3 = 1. Among other examples, extremal binary self-dual codes of length 66 are obtained by these constructions. These are extended by using extension theorems for self-dual codes and as a result 8 new extremal binary self-dual codes of length 68 are obtained. More precisely, codes with beta=117, 120, 133 in W68;1 and with gamma = 1, beta=49, 57, 59 and codes with gamma=2, beta=69, 81 in W68;2 are constructed for the ?first time in the literature. In addition to these, some known such codes are reconstructed via this extension. The results are tabulated.
Anahtar Kelimeler
Kaynakça
- 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), 1319-1333, 1990.
- S. T. Dougherty, T. A. Gulliver, M., Harada, Extremal binary self dual codes, IEEE Trans. Inform. Theory, 43(6), 2036-2047, 1997.
- P. Gaborit, Quadratic double circulant codes over fields, Journal of Combinatorial Theory Series A, 97(1), 85-107, 2002.
- W.C. Huffman, V. Pless, Fundamentals of error correcting codes, Cambridge University press, 2003.
- J.-L. Kim, New extremal self-dual codes of lengths 36, 38 and 58, IEEE Trans. Inf. Theory, 47(1), 386-393, 2001.
- A. Kaya, B. Yildiz, İ. Şiap, New extremal binary self-dual codes from F4+ uF4-lifts of quadratic double circulant codes over F, available online at http://arxiv.org/abs/1405.7147
- A. Kaya, B. Yildiz, Binary generator matrices of new extremal self-dual binary codes of length 68, available online at http://www.fatih.edu.tr/~akaya/binary/68u31.txt
- A. Kaya, B. Yildiz, Extension theorems for self-dual codes over rings and new binary self-dual codes, available online at http://arxiv.org/abs/1404.0195.
- E. M. Rains, Shadow Bounds for Self Dual Codes, IEEE Trans. Inf. Theory, 44(1), 134-139, 1998.
- H.-P. Tsai, P.-Y. Shih, R.-Y. Wuh, W.-K. Su, C.-H. Chen, Construction of self-dual codes, IEEE
- Trans. Inform. Theory, 54(8), 3826-3831, 2008.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Mart 2014 |
| Yayımlandığı Sayı | Yıl 2014 Cilt: 1 Sayı: 1 |