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Some connections between self-dual codes, combinatorial designs and secret sharing schemes
Symmetric designs possessing tactical decompositions
1. | University of Zagreb, Faculty of Electrical Engineering and Computing, Department of Applied Mathematics, Unska 3, 10000 Zagreb, Croatia, Croatia |
References:
[1] |
W. O. Alltop, An infinite class of $5$-designs, J. Combin. Theory Ser. A, 12 (1972), 390-395.
doi: 10.1016/0097-3165(72)90104-5. |
[2] |
I. Bouyukliev, V. Fack and J. Winne, $2$-$(31,15,7)$, $2$-$(35,17,8)$ and $2$-$(36,15,6)$ designs with automorphisms of odd prime order, and their related Hadamard matrices and codes, Des. Codes Crypt., 51 (2009), 105-122.
doi: 10.1007/s10623-008-9247-x. |
[3] |
D. Crnković and D. Held, Some Menon designs having $U(3,3)$ as an automorphism group, Illinois J. Math., 47 (2003), 129-139. |
[4] |
V. Ćepulić, On symmetric block designs $(40,13,4)$ with automorphisms of order $5$, Discrete Math., 128 (1994), 45-60.
doi: 10.1016/0012-365X(94)90103-1. |
[5] |
D. Held, J. Hrabe de Angelis and M.-O. Pavčević, $PSp_4(3)$ as a symmetric $(36,15,6)$ design, Rend. Sem. Mat. Univ. Padova, 101 (1999), 95-98. |
[6] |
D. Held and M.-O. Pavčević, Symmetric $(79,27,9)$ design admitting a faithful action of a Frobenius group of order $39$, Europ. J. Combinatorics, 18 (1997), 409-416.
doi: 10.1006/eujc.1996.0103. |
[7] |
Y. J. Ionin and T. van Trung, Symmetric designs, in "CRC Handbook of Combinatorial Designs'' (eds. C.J. Colbourn and J.H. Dinitz), 2nd edition, CRC Press, Boca Raton, FL, (2007), 110-124. |
[8] |
Z. Janko and T. van Trung, Construction of a new symmetric block design for $(78,22,6)$ with the help of tactical decompositions, J. Combin. Theory Ser. A, 40 (1985), 451-455.
doi: 10.1016/0097-3165(85)90107-4. |
[9] |
P. Kaski and P. R. J. Östergärd, "Classification Algorithms for Codes and Designs,'' Springer, Berlin, 2006. |
[10] |
V. Krčadinac, Steiner $2$-designs $S(2,5,41)$ with automorphisms of order $3$, J. Combin. Math. Combin. Comput., 43 (2002), 83-99. |
[11] |
E. Lander, "Symmetric Designs: An Algebraic Approach,'' Cambridge University Press, Cambridge, 1983.
doi: 10.1017/CBO9780511662164. |
[12] |
R. Mathon and A. Rosa, $2$-$(v,k,\lambda)$ designs of small order, in "CRC Handbook of Combinatorial Designs'' (eds. C.J. Colbourn and J.H. Dinitz), 2nd edition, CRC Press, Boca Raton, FL, (2007), 25-58. |
[13] |
B. D. McKay, Nauty user's guide (version 1.5), Technical Report TR-CS-90-02, Dep. Computer Science, Australian National University, 1990. |
show all references
References:
[1] |
W. O. Alltop, An infinite class of $5$-designs, J. Combin. Theory Ser. A, 12 (1972), 390-395.
doi: 10.1016/0097-3165(72)90104-5. |
[2] |
I. Bouyukliev, V. Fack and J. Winne, $2$-$(31,15,7)$, $2$-$(35,17,8)$ and $2$-$(36,15,6)$ designs with automorphisms of odd prime order, and their related Hadamard matrices and codes, Des. Codes Crypt., 51 (2009), 105-122.
doi: 10.1007/s10623-008-9247-x. |
[3] |
D. Crnković and D. Held, Some Menon designs having $U(3,3)$ as an automorphism group, Illinois J. Math., 47 (2003), 129-139. |
[4] |
V. Ćepulić, On symmetric block designs $(40,13,4)$ with automorphisms of order $5$, Discrete Math., 128 (1994), 45-60.
doi: 10.1016/0012-365X(94)90103-1. |
[5] |
D. Held, J. Hrabe de Angelis and M.-O. Pavčević, $PSp_4(3)$ as a symmetric $(36,15,6)$ design, Rend. Sem. Mat. Univ. Padova, 101 (1999), 95-98. |
[6] |
D. Held and M.-O. Pavčević, Symmetric $(79,27,9)$ design admitting a faithful action of a Frobenius group of order $39$, Europ. J. Combinatorics, 18 (1997), 409-416.
doi: 10.1006/eujc.1996.0103. |
[7] |
Y. J. Ionin and T. van Trung, Symmetric designs, in "CRC Handbook of Combinatorial Designs'' (eds. C.J. Colbourn and J.H. Dinitz), 2nd edition, CRC Press, Boca Raton, FL, (2007), 110-124. |
[8] |
Z. Janko and T. van Trung, Construction of a new symmetric block design for $(78,22,6)$ with the help of tactical decompositions, J. Combin. Theory Ser. A, 40 (1985), 451-455.
doi: 10.1016/0097-3165(85)90107-4. |
[9] |
P. Kaski and P. R. J. Östergärd, "Classification Algorithms for Codes and Designs,'' Springer, Berlin, 2006. |
[10] |
V. Krčadinac, Steiner $2$-designs $S(2,5,41)$ with automorphisms of order $3$, J. Combin. Math. Combin. Comput., 43 (2002), 83-99. |
[11] |
E. Lander, "Symmetric Designs: An Algebraic Approach,'' Cambridge University Press, Cambridge, 1983.
doi: 10.1017/CBO9780511662164. |
[12] |
R. Mathon and A. Rosa, $2$-$(v,k,\lambda)$ designs of small order, in "CRC Handbook of Combinatorial Designs'' (eds. C.J. Colbourn and J.H. Dinitz), 2nd edition, CRC Press, Boca Raton, FL, (2007), 25-58. |
[13] |
B. D. McKay, Nauty user's guide (version 1.5), Technical Report TR-CS-90-02, Dep. Computer Science, Australian National University, 1990. |
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