August  2011, 5(3): 417-424. doi: 10.3934/amc.2011.5.417

Some new distance-4 constant weight codes

1. 

Dept. of Math., Techn. Univ. Eindhoven, P. O. Box 513, 5600MB Eindhoven, Netherlands

2. 

Department of Computer Science, Technion, Haifa 32000

Received  March 2010 Revised  February 2011 Published  August 2011

Improved binary constant weight codes with minimum distance 4 are constructed. A table with bounds on the chromatic number of small Johnson graphs is given.
Citation: Andries E. Brouwer, Tuvi Etzion. Some new distance-4 constant weight codes. Advances in Mathematics of Communications, 2011, 5 (3) : 417-424. doi: 10.3934/amc.2011.5.417
References:
[1]

, http://www.win.tue.nl/~aeb/codes/andw.html  

[2]

A. Betten, R. Laue and A. Wassermann, A Steiner 5-design on 36 points, Des. Codes Crypt., 17 (1999), 181-186. doi: 10.1023/A:1026427226213.

[3]

A. E. Brouwer, J. B. Shearer, N. J. A. Sloane and W. D. Smith, A new table of constant weight codes, IEEE Trans. Inform. Theory, 36 (1990), 1334-1380. doi: 10.1109/18.59932.

[4]

R. H. F. Denniston, Sylvester's problem of the 15 school-girls, Discr. Math., 9 (1974), 229-233. doi: 10.1016/0012-365X(74)90004-1.

[5]

R. H. F. Denniston, Some new 5-designs, Bull. London Math. Soc., 8 (1976), 263-267. doi: 10.1112/blms/8.3.263.

[6]

T. Etzion, Optimal partitions for triples, J. Combin. Theory (A), 59 (1992), 161-176. doi: 10.1016/0097-3165(92)90062-Y.

[7]

T. Etzion, Partitions of triples into optimal packings, J. Combin. Theory (A), 59 (1992), 269-284. doi: 10.1016/0097-3165(92)90069-7.

[8]

T. Etzion, Partitions for quadruples, Ars Combin., 36 (1993), 296-308.

[9]

T. Etzion and S. Bitan, On the chromatic number, colorings, and codes of the Johnson graph, Discr. Appl. Math., 70 (1996), 163-175. doi: 10.1016/0166-218X(96)00104-7.

[10]

T. Etzion and P. R. J. Östergård, Greedy and heuristic algorithms for codes and colorings, IEEE Trans. Inform. Theory, 44 (1998), 382-388. doi: 10.1109/18.651069.

[11]

T. Etzion and C. L. M. van Pul, New lower bounds for constant weight codes, IEEE Trans. Inform. Theory, 35 (1989), 1324-1329. doi: 10.1109/18.45293.

[12]

R. L. Graham and N. J. A. Sloane, Lower bounds for constant weight codes, IEEE Trans. Inform. Theory, 26 (1980), 37-43. doi: 10.1109/TIT.1980.1056141.

[13]

L. J. Ji, A new existence proof for large sets of disjoint Steiner triple systems, J. Combin. Theory (A), 112 (2005), 308-327. doi: 10.1016/j.jcta.2005.06.005.

[14]

L. J. Ji, Partition of triples of order $6k+5$ into $6k+3$ optimal packings and one packing of size $8k+4$, Graphs Combin., 22 (2006), 251-260. doi: 10.1007/s00373-005-0632-1.

[15]

J. X. Lu, On large sets of disjoint Steiner triple systems I, II, III, J. Combin. Theory (A), 34 (1983), 140-146, 147-155, 156-183, and IV, V, VI, ibid., 37 (1984), 136-163, 164-188, 189-192.

[16]

N. S. Mendelsohn and S. H. Y. Hung, On the Steiner systems $S(3,4,14)$ and $S(4,5,15)$, Utilitas Math., 1 (1972), 5-95.

[17]

K. J. Nurmela, M. K. Kaikkonen and P. R. J. Östergård, New constant weight codes from linear permutation groups, IEEE Trans. Inform. Theory, 43 (1997), 1623-1630, doi: 10.1109/18.623163.

[18]

D. H. Smith, L. A. Hughes and S. Perkins, A new table of constant weight codes of length greater than 28, Electronic J. Combin., 13 (2006), #A2.

[19]

L. Teirlinck, A completion of Lu's determination of the spectrum of large sets of disjoint Steiner Triple systems, J. Combin. Theory (A), 57 (1991), 302-305. doi: 10.1016/0097-3165(91)90053-J.

show all references

References:
[1]

, http://www.win.tue.nl/~aeb/codes/andw.html  

[2]

A. Betten, R. Laue and A. Wassermann, A Steiner 5-design on 36 points, Des. Codes Crypt., 17 (1999), 181-186. doi: 10.1023/A:1026427226213.

[3]

A. E. Brouwer, J. B. Shearer, N. J. A. Sloane and W. D. Smith, A new table of constant weight codes, IEEE Trans. Inform. Theory, 36 (1990), 1334-1380. doi: 10.1109/18.59932.

[4]

R. H. F. Denniston, Sylvester's problem of the 15 school-girls, Discr. Math., 9 (1974), 229-233. doi: 10.1016/0012-365X(74)90004-1.

[5]

R. H. F. Denniston, Some new 5-designs, Bull. London Math. Soc., 8 (1976), 263-267. doi: 10.1112/blms/8.3.263.

[6]

T. Etzion, Optimal partitions for triples, J. Combin. Theory (A), 59 (1992), 161-176. doi: 10.1016/0097-3165(92)90062-Y.

[7]

T. Etzion, Partitions of triples into optimal packings, J. Combin. Theory (A), 59 (1992), 269-284. doi: 10.1016/0097-3165(92)90069-7.

[8]

T. Etzion, Partitions for quadruples, Ars Combin., 36 (1993), 296-308.

[9]

T. Etzion and S. Bitan, On the chromatic number, colorings, and codes of the Johnson graph, Discr. Appl. Math., 70 (1996), 163-175. doi: 10.1016/0166-218X(96)00104-7.

[10]

T. Etzion and P. R. J. Östergård, Greedy and heuristic algorithms for codes and colorings, IEEE Trans. Inform. Theory, 44 (1998), 382-388. doi: 10.1109/18.651069.

[11]

T. Etzion and C. L. M. van Pul, New lower bounds for constant weight codes, IEEE Trans. Inform. Theory, 35 (1989), 1324-1329. doi: 10.1109/18.45293.

[12]

R. L. Graham and N. J. A. Sloane, Lower bounds for constant weight codes, IEEE Trans. Inform. Theory, 26 (1980), 37-43. doi: 10.1109/TIT.1980.1056141.

[13]

L. J. Ji, A new existence proof for large sets of disjoint Steiner triple systems, J. Combin. Theory (A), 112 (2005), 308-327. doi: 10.1016/j.jcta.2005.06.005.

[14]

L. J. Ji, Partition of triples of order $6k+5$ into $6k+3$ optimal packings and one packing of size $8k+4$, Graphs Combin., 22 (2006), 251-260. doi: 10.1007/s00373-005-0632-1.

[15]

J. X. Lu, On large sets of disjoint Steiner triple systems I, II, III, J. Combin. Theory (A), 34 (1983), 140-146, 147-155, 156-183, and IV, V, VI, ibid., 37 (1984), 136-163, 164-188, 189-192.

[16]

N. S. Mendelsohn and S. H. Y. Hung, On the Steiner systems $S(3,4,14)$ and $S(4,5,15)$, Utilitas Math., 1 (1972), 5-95.

[17]

K. J. Nurmela, M. K. Kaikkonen and P. R. J. Östergård, New constant weight codes from linear permutation groups, IEEE Trans. Inform. Theory, 43 (1997), 1623-1630, doi: 10.1109/18.623163.

[18]

D. H. Smith, L. A. Hughes and S. Perkins, A new table of constant weight codes of length greater than 28, Electronic J. Combin., 13 (2006), #A2.

[19]

L. Teirlinck, A completion of Lu's determination of the spectrum of large sets of disjoint Steiner Triple systems, J. Combin. Theory (A), 57 (1991), 302-305. doi: 10.1016/0097-3165(91)90053-J.

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