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Asymptotic lower bound on the algebraic immunity of random balanced multi-output Boolean functions
New extremal binary self-dual codes of length $68$ from $R_2$-lifts of binary self-dual codes
1. | Department of Mathematics, Fatih University, 34500, Istanbul |
References:
[1] |
W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput., 24 (1997), 235-265.
doi: 10.1006/jsco.1996.0125. |
[2] |
S. Bouyuklieva, Some Optimal self-orthogonal and self-dual codes, J. Discrete Math., 287 (2004), 1-10.
doi: 10.1016/j.disc.2004.06.010. |
[3] |
S. Bouyuklieva and I. Boukliev, Extremal self-dual codes with an automorphism of order 2, IEEE Trans. Inform. Theory, 44 (1998), 323-328.
doi: 10.1109/18.651059. |
[4] |
S. Bouyuklieva, N. Yankov and J.-L. Kim, Classification of binary self-dual [48,24,10]-codes with an automorphism odd prime order, Finite Fields Appl., 18 (2012), 1104-1113.
doi: 10.1016/j.ffa.2012.08.002. |
[5] |
J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, 36 (1990), 1319-1333.
doi: 10.1109/18.59931. |
[6] |
S. T. Dougherty, A. Gulliver and M. Harada, Extremal binary self-dual codes, IEEE Trans. Infrom. Theory, 43 (1997), 2036-2047.
doi: 10.1109/18.641574. |
[7] |
S. T. Dougherty, J.-L. Kim, H. Kulosman and H. Liu, Self-dual codes over commutative Frobenius rings, Finite Fields Appl., 16 (2010), 4-26.
doi: 10.1016/j.ffa.2009.11.003. |
[8] |
S. T. Dougherty, J.-L. Kim and H. Liu, Constructions of self-dual codes over finite commutative chain rings, J. Inform. Coding Theory, 1 (2010), 171-190.
doi: 10.1504/IJICOT.2010.032133. |
[9] |
S. T. Dougherty, B. Yildiz and S. Karadeniz, Codes over $R_k$, Gray maps and their binary images, Finite Fields Appl., 17 (2011), 205-219.
doi: 10.1016/j.ffa.2010.11.002. |
[10] |
S. T. Dougherty, B. Yildiz and S. Karadeniz, Self-dual codes over $R_k$ and binary self-dual codes, European J. Pure Appl. Math., 6 (2013), 89-106. |
[11] |
P. Gaborit and A. Otmani, Experimental constructions of self-dual codes, Finite Fields Appl., 9 (2003), 372-394.
doi: 10.1016/S1071-5797(03)00011-X. |
[12] |
S. Karadeniz and B. Yildiz, $R_2$-generator matrices for extremal self-dual codes of length 68,, available online at \url{http://www.fatih.edu.tr/~akaya/NewSelf-dual68.pdf}, ().
|
[13] |
S. Karadeniz and B. Yildiz, Double-circulant and double-bordered-circulant constructions for self-dual codes over $R_2$, Adv. Math. Commun., 6 (2012), 193-202.
doi: 10.3934/amc.2012.6.193. |
[14] |
S. Karadeniz and B. Yildiz, New extremal binary self-dual codes of length $64$ as $R_3$-lifts of the extended binary Hamming code,, submitted., ().
|
[15] |
H. H. Kim, H. Lee, J. B. Lee and Y. Lee, Construction of self-dual codes with an automorpihsm of of order $p$, Adv. Math. Commun., 5 (2011), 23-36.
doi: 10.3934/amc.2011.5.23. |
[16] |
A. Munemasa, Database of self-dual codes,, available online at \url{http://www.math.is.tohoku.ac.jp/~munemasa/research/codes/data/2/18.magma}, ().
|
[17] |
T. Nishimura, A new extremal self-dual code of length 64, IEEE Trans. Inform. Theory, 50 (2004), 2173-2174.
doi: 10.1109/TIT.2004.833359. |
[18] |
E. M. Rains, Shadow bounds for self dual codes, IEEE Trans. Inform. Theory, 44 (1998), 134-139.
doi: 10.1109/18.651000. |
[19] |
H. P. Tsai, P. Y. Shih, R. Y. Wuh, W. K. Su and C. H. Chen, Construction of self-dual codes, IEEE Trans. Inform. Theory, 54 (2008), 3826-3831.
doi: 10.1109/TIT.2008.926454. |
[20] |
J. Wood, Duality for modules over finite rings and applications to coding theory, Amer. J. Math., 121 (1999), 555-575.
doi: 10.1353/ajm.1999.0024. |
[21] |
B. Yildiz and S. Karadeniz, Linear codes over $\mathbb F_2+u\mathbb F_2+v\mathbb F_2+uv\mathbb F_2$, Des. Codes Crypt., 54 (2010), 61-81.
doi: 10.1007/s10623-009-9309-8. |
[22] |
B. Yildiz and S. Karadeniz, Self-dual codes over $\mathbb F_2+u\mathbb F_2+v\mathbb F_2+uv\mathbb F_2$, J. Franklin Inst., 347 (2010), 1888-1894.
doi: 10.1016/j.jfranklin.2010.10.007. |
show all references
References:
[1] |
W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput., 24 (1997), 235-265.
doi: 10.1006/jsco.1996.0125. |
[2] |
S. Bouyuklieva, Some Optimal self-orthogonal and self-dual codes, J. Discrete Math., 287 (2004), 1-10.
doi: 10.1016/j.disc.2004.06.010. |
[3] |
S. Bouyuklieva and I. Boukliev, Extremal self-dual codes with an automorphism of order 2, IEEE Trans. Inform. Theory, 44 (1998), 323-328.
doi: 10.1109/18.651059. |
[4] |
S. Bouyuklieva, N. Yankov and J.-L. Kim, Classification of binary self-dual [48,24,10]-codes with an automorphism odd prime order, Finite Fields Appl., 18 (2012), 1104-1113.
doi: 10.1016/j.ffa.2012.08.002. |
[5] |
J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, 36 (1990), 1319-1333.
doi: 10.1109/18.59931. |
[6] |
S. T. Dougherty, A. Gulliver and M. Harada, Extremal binary self-dual codes, IEEE Trans. Infrom. Theory, 43 (1997), 2036-2047.
doi: 10.1109/18.641574. |
[7] |
S. T. Dougherty, J.-L. Kim, H. Kulosman and H. Liu, Self-dual codes over commutative Frobenius rings, Finite Fields Appl., 16 (2010), 4-26.
doi: 10.1016/j.ffa.2009.11.003. |
[8] |
S. T. Dougherty, J.-L. Kim and H. Liu, Constructions of self-dual codes over finite commutative chain rings, J. Inform. Coding Theory, 1 (2010), 171-190.
doi: 10.1504/IJICOT.2010.032133. |
[9] |
S. T. Dougherty, B. Yildiz and S. Karadeniz, Codes over $R_k$, Gray maps and their binary images, Finite Fields Appl., 17 (2011), 205-219.
doi: 10.1016/j.ffa.2010.11.002. |
[10] |
S. T. Dougherty, B. Yildiz and S. Karadeniz, Self-dual codes over $R_k$ and binary self-dual codes, European J. Pure Appl. Math., 6 (2013), 89-106. |
[11] |
P. Gaborit and A. Otmani, Experimental constructions of self-dual codes, Finite Fields Appl., 9 (2003), 372-394.
doi: 10.1016/S1071-5797(03)00011-X. |
[12] |
S. Karadeniz and B. Yildiz, $R_2$-generator matrices for extremal self-dual codes of length 68,, available online at \url{http://www.fatih.edu.tr/~akaya/NewSelf-dual68.pdf}, ().
|
[13] |
S. Karadeniz and B. Yildiz, Double-circulant and double-bordered-circulant constructions for self-dual codes over $R_2$, Adv. Math. Commun., 6 (2012), 193-202.
doi: 10.3934/amc.2012.6.193. |
[14] |
S. Karadeniz and B. Yildiz, New extremal binary self-dual codes of length $64$ as $R_3$-lifts of the extended binary Hamming code,, submitted., ().
|
[15] |
H. H. Kim, H. Lee, J. B. Lee and Y. Lee, Construction of self-dual codes with an automorpihsm of of order $p$, Adv. Math. Commun., 5 (2011), 23-36.
doi: 10.3934/amc.2011.5.23. |
[16] |
A. Munemasa, Database of self-dual codes,, available online at \url{http://www.math.is.tohoku.ac.jp/~munemasa/research/codes/data/2/18.magma}, ().
|
[17] |
T. Nishimura, A new extremal self-dual code of length 64, IEEE Trans. Inform. Theory, 50 (2004), 2173-2174.
doi: 10.1109/TIT.2004.833359. |
[18] |
E. M. Rains, Shadow bounds for self dual codes, IEEE Trans. Inform. Theory, 44 (1998), 134-139.
doi: 10.1109/18.651000. |
[19] |
H. P. Tsai, P. Y. Shih, R. Y. Wuh, W. K. Su and C. H. Chen, Construction of self-dual codes, IEEE Trans. Inform. Theory, 54 (2008), 3826-3831.
doi: 10.1109/TIT.2008.926454. |
[20] |
J. Wood, Duality for modules over finite rings and applications to coding theory, Amer. J. Math., 121 (1999), 555-575.
doi: 10.1353/ajm.1999.0024. |
[21] |
B. Yildiz and S. Karadeniz, Linear codes over $\mathbb F_2+u\mathbb F_2+v\mathbb F_2+uv\mathbb F_2$, Des. Codes Crypt., 54 (2010), 61-81.
doi: 10.1007/s10623-009-9309-8. |
[22] |
B. Yildiz and S. Karadeniz, Self-dual codes over $\mathbb F_2+u\mathbb F_2+v\mathbb F_2+uv\mathbb F_2$, J. Franklin Inst., 347 (2010), 1888-1894.
doi: 10.1016/j.jfranklin.2010.10.007. |
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