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Some connections between self-dual codes, combinatorial designs and secret sharing schemes
1. | Department of Mathematics and Informatics, Veliko Tarnovo University, Bulgaria, Bulgaria |
References:
[1] |
E. F. Assmus and H. F. Mattson, New $5$-designs, J. Combin. Theory, 6 (1969), 122-151.
doi: 10.1016/S0021-9800(69)80115-8. |
[2] |
S. Bouyuklieva and M. Harada, Extremal self-dual $[50,25,10]$ codes with automorphisms of order $3$ and quasi-symmetric $2-(49,9,6)$ designs, Des. Codes Crypt., 28 (2003), 163-169.
doi: 10.1023/A:1022588407585. |
[3] |
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. |
[4] |
S. T. Dougherty, S. Mesnager and P. Solé, Secret-sharing schemes based on self-dual codes, in "Information Theory Workshop,'' Porto, (2008), 338-342. |
[5] |
W.C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Appl., 11 (2005), 451-490.
doi: 10.1016/j.ffa.2005.05.012. |
[6] |
W. C. Huffman and V. Pless, "Fundamentals of Error-Correcting Codes,'' Cambridge Univ. Press, 2003. |
[7] |
J. L. Massey, Some applications of coding theory in cryptography, in "Codes and Ciphers, Cryptography and Coding IV'' (ed. P.G. Farrell), Formara Lt, Esses, England, (1995), 33-47. |
[8] |
E. M. Rains, Shadow bounds for self-dual-codes, IEEE Trans. Inform. Theory, 44 (1998), 134-139.
doi: 10.1109/18.651000. |
show all references
References:
[1] |
E. F. Assmus and H. F. Mattson, New $5$-designs, J. Combin. Theory, 6 (1969), 122-151.
doi: 10.1016/S0021-9800(69)80115-8. |
[2] |
S. Bouyuklieva and M. Harada, Extremal self-dual $[50,25,10]$ codes with automorphisms of order $3$ and quasi-symmetric $2-(49,9,6)$ designs, Des. Codes Crypt., 28 (2003), 163-169.
doi: 10.1023/A:1022588407585. |
[3] |
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. |
[4] |
S. T. Dougherty, S. Mesnager and P. Solé, Secret-sharing schemes based on self-dual codes, in "Information Theory Workshop,'' Porto, (2008), 338-342. |
[5] |
W.C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Appl., 11 (2005), 451-490.
doi: 10.1016/j.ffa.2005.05.012. |
[6] |
W. C. Huffman and V. Pless, "Fundamentals of Error-Correcting Codes,'' Cambridge Univ. Press, 2003. |
[7] |
J. L. Massey, Some applications of coding theory in cryptography, in "Codes and Ciphers, Cryptography and Coding IV'' (ed. P.G. Farrell), Formara Lt, Esses, England, (1995), 33-47. |
[8] |
E. M. Rains, Shadow bounds for self-dual-codes, IEEE Trans. Inform. Theory, 44 (1998), 134-139.
doi: 10.1109/18.651000. |
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