Some new distance-4 constant weight codes

Previous Article
AMC Home
This Issue
Next Article
$\mathbb{Z}_2\mathbb{Z}_4$-additive perfect codes in Steganography

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

Some new distance-4 constant weight codes

Andries E. Brouwer ^1, and Tuvi Etzion ^2,

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

Abstract
Related Papers

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.

Keywords: Binary constant weight code..

Mathematics Subject Classification: Primary: 94B60; Secondary: 05E30, 05C1.

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. 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. doi: 10.1109/18.59932.
[4]	R. H. F. Denniston, Sylvester's problem of the 15 school-girls,, Discr. Math., 9 (1974), 229. doi: 10.1016/0012-365X(74)90004-1.
[5]	R. H. F. Denniston, Some new 5-designs,, Bull. London Math. Soc., 8 (1976), 263. doi: 10.1112/blms/8.3.263.
[6]	T. Etzion, Optimal partitions for triples,, J. Combin. Theory (A), 59 (1992), 161. doi: 10.1016/0097-3165(92)90062-Y.
[7]	T. Etzion, Partitions of triples into optimal packings,, J. Combin. Theory (A), 59 (1992), 269. doi: 10.1016/0097-3165(92)90069-7.
[8]	T. Etzion, Partitions for quadruples,, Ars Combin., 36 (1993), 296.
[9]	T. Etzion and S. Bitan, On the chromatic number, colorings, and codes of the Johnson graph,, Discr. Appl. Math., 70 (1996), 163. 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. 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. 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. 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. 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. 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.
[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.
[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. 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).
[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. 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. 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. doi: 10.1109/18.59932.
[4]	R. H. F. Denniston, Sylvester's problem of the 15 school-girls,, Discr. Math., 9 (1974), 229. doi: 10.1016/0012-365X(74)90004-1.
[5]	R. H. F. Denniston, Some new 5-designs,, Bull. London Math. Soc., 8 (1976), 263. doi: 10.1112/blms/8.3.263.
[6]	T. Etzion, Optimal partitions for triples,, J. Combin. Theory (A), 59 (1992), 161. doi: 10.1016/0097-3165(92)90062-Y.
[7]	T. Etzion, Partitions of triples into optimal packings,, J. Combin. Theory (A), 59 (1992), 269. doi: 10.1016/0097-3165(92)90069-7.
[8]	T. Etzion, Partitions for quadruples,, Ars Combin., 36 (1993), 296.
[9]	T. Etzion and S. Bitan, On the chromatic number, colorings, and codes of the Johnson graph,, Discr. Appl. Math., 70 (1996), 163. 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. 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. 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. 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. 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. 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.
[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.
[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. 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).
[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. doi: 10.1016/0097-3165(91)90053-J.

[1]	Denis S. Krotov, Patric R. J. Östergård, Olli Pottonen. Non-existence of a ternary constant weight $(16,5,15;2048)$ diameter perfect code. Advances in Mathematics of Communications, 2016, 10 (2) : 393-399. doi: 10.3934/amc.2016013
[2]	Masaaki Harada, Ethan Novak, Vladimir D. Tonchev. The weight distribution of the self-dual $[128,64]$ polarity design code. Advances in Mathematics of Communications, 2016, 10 (3) : 643-648. doi: 10.3934/amc.2016032
[3]	Nicolay M. Tanushev, Luminita Vese. A piecewise-constant binary model for electrical impedance tomography. Inverse Problems & Imaging, 2007, 1 (2) : 423-435. doi: 10.3934/ipi.2007.1.423
[4]	Andreas Klein, Leo Storme. On the non-minimality of the largest weight codewords in the binary Reed-Muller codes. Advances in Mathematics of Communications, 2011, 5 (2) : 333-337. doi: 10.3934/amc.2011.5.333
[5]	Daniel Heinlein, Michael Kiermaier, Sascha Kurz, Alfred Wassermann. A subspace code of size $ \bf{333} $ in the setting of a binary $ \bf{q} $-analog of the Fano plane. Advances in Mathematics of Communications, 2019, 13 (3) : 457-475. doi: 10.3934/amc.2019029
[6]	Laura Luzzi, Ghaya Rekaya-Ben Othman, Jean-Claude Belfiore. Algebraic reduction for the Golden Code. Advances in Mathematics of Communications, 2012, 6 (1) : 1-26. doi: 10.3934/amc.2012.6.1
[7]	Irene Márquez-Corbella, Edgar Martínez-Moro, Emilio Suárez-Canedo. On the ideal associated to a linear code. Advances in Mathematics of Communications, 2016, 10 (2) : 229-254. doi: 10.3934/amc.2016003
[8]	Serhii Dyshko. On extendability of additive code isometries. Advances in Mathematics of Communications, 2016, 10 (1) : 45-52. doi: 10.3934/amc.2016.10.45
[9]	Fengwei Li, Qin Yue, Fengmei Liu. The weight distributions of constacyclic codes. Advances in Mathematics of Communications, 2017, 11 (3) : 471-480. doi: 10.3934/amc.2017039
[10]	Tim Alderson, Alessandro Neri. Maximum weight spectrum codes. Advances in Mathematics of Communications, 2019, 13 (1) : 101-119. doi: 10.3934/amc.2019006
[11]	Olof Heden. The partial order of perfect codes associated to a perfect code. Advances in Mathematics of Communications, 2007, 1 (4) : 399-412. doi: 10.3934/amc.2007.1.399
[12]	Selim Esedoḡlu, Fadil Santosa. Error estimates for a bar code reconstruction method. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1889-1902. doi: 10.3934/dcdsb.2012.17.1889
[13]	Miriam Manoel, Patrícia Tempesta. Binary differential equations with symmetries. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 1957-1974. doi: 10.3934/dcds.2019082
[14]	Chengju Li, Sunghan Bae, Shudi Yang. Some two-weight and three-weight linear codes. Advances in Mathematics of Communications, 2019, 13 (1) : 195-211. doi: 10.3934/amc.2019013
[15]	Petr Lisoněk, Layla Trummer. Algorithms for the minimum weight of linear codes. Advances in Mathematics of Communications, 2016, 10 (1) : 195-207. doi: 10.3934/amc.2016.10.195
[16]	Alexander Barg, Arya Mazumdar, Gilles Zémor. Weight distribution and decoding of codes on hypergraphs. Advances in Mathematics of Communications, 2008, 2 (4) : 433-450. doi: 10.3934/amc.2008.2.433
[17]	Diana M. Thomas, Ashley Ciesla, James A. Levine, John G. Stevens, Corby K. Martin. A mathematical model of weight change with adaptation. Mathematical Biosciences & Engineering, 2009, 6 (4) : 873-887. doi: 10.3934/mbe.2009.6.873
[18]	Lluís Alsedà, Michał Misiurewicz. Semiconjugacy to a map of a constant slope. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3403-3413. doi: 10.3934/dcdsb.2015.20.3403
[19]	Joaquim Borges, Ivan Yu. Mogilnykh, Josep Rifà, Faina I. Solov'eva. Structural properties of binary propelinear codes. Advances in Mathematics of Communications, 2012, 6 (3) : 329-346. doi: 10.3934/amc.2012.6.329
[20]	Karma Dajani, Cor Kraaikamp, Pierre Liardet. Ergodic properties of signed binary expansions. Discrete & Continuous Dynamical Systems - A, 2006, 15 (1) : 87-119. doi: 10.3934/dcds.2006.15.87

2017 Impact Factor: 0.564

American Institute of Mathematical Sciences