The Sizes of Optimal $q$ -Ary Codes of Weight Three and Distance Four: A Complete Solution

This correspondence introduces two new constructive techniques to complete the determination of the sizes of optimal q-ary codes of constant weight three and distance four.

[1]  Yeow Meng Chee,et al.  Constructions for $q$-Ary Constant-Weight Codes , 2007, IEEE Transactions on Information Theory.

[2]  Dianhua Wu,et al.  4‐*GDDs(3n) and generalized Steiner systems GS(2, 4, v, 3) , 2003 .

[3]  D. Wu,et al.  4-* GDDs ( 3 n ) and Generalized Steiner Systems GS , 2003 .

[4]  Michael Langberg,et al.  The encoding complexity of network coding , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[5]  Wu Dian-hua Generalized Steiner Triple Systems with Group Size Ten , 2003 .

[6]  Ge Gennian,et al.  Some new optimal quaternary constant weight codes , 2005 .

[7]  T. Ho,et al.  On Linear Network Coding , 2010 .

[8]  Luc Teirlinck Large sets with holes , 1993 .

[9]  Denis S. Krotov Inductive Constructions of Perfect Ternary Constant-Weight Codes with Distance 3 , 2001, Probl. Inf. Transm..

[10]  Tuvi Etzion,et al.  Optimal constant weight codes over Zk and generalized designs , 1997, Discret. Math..

[11]  Kevin T. Phelps,et al.  Constant Weight Codes and Group Divisible Designs , 1999, Des. Codes Cryptogr..

[12]  Kevin T. Phelps,et al.  Generalized Steiner Systems With Block Size Three and Group Size Four , 1999, Ars Comb..

[13]  Torleiv Kløve,et al.  On the Svanström bound for ternary constant-weight codes , 2001, IEEE Trans. Inf. Theory.

[14]  A. J. Han Vinck,et al.  On the Constructions of Constant-Weight Codes , 1998, IEEE Trans. Inf. Theory.

[15]  Gennian Ge,et al.  Generalized Steiner Triple Systems with Group Size g = 7, 8 , 2000, Ars Comb..

[16]  Gennian Ge,et al.  Generalized Steiner systems GS4 (2, 4, v, g) for g = 2, 3, 6 , 2001 .

[17]  Kevin T. Phelps,et al.  Generalized Steiner systems with block size three and group sizeg ? 3(mod 6) , 1997 .

[18]  Dianhua Wu,et al.  Generalized Steiner systems GS5(2, 5, v, 5) , 2006, Australas. J Comb..

[19]  Gennian Ge,et al.  Generalized steiner triple systems with group size five , 1999 .

[20]  Mattias Svanström A lower bound for ternary constant weight codes , 1997, IEEE Trans. Inf. Theory.

[21]  Mattias Svanström A Class of Perfect Ternary Constant-Weight Codes , 1999, Des. Codes Cryptogr..

[22]  Gennian Ge Generalized Steiner Triple Systems with Group Size g ≡ 0,3 (mod 6) , 2000, Australas. J Comb..

[23]  Jianxing Yin,et al.  Maximum distance holey packings and related codes , 1999 .

[24]  Gennian Ge,et al.  Some new optimal quaternary constant weight codes , 2007, Science in China Series F: Information Sciences.

[25]  Galina Bogdanova NEW BOUNDS FOR THE MAXIMUM SIZE OF TERNARY CONSTANT WEIGHT CODES , 2000 .

[26]  Donald L. Kreher,et al.  Combinatorial algorithms: generation, enumeration, and search , 1998, SIGA.

[27]  Patric R. J. Östergård,et al.  Ternary Constant Weight Codes , 2002, Electron. J. Comb..

[28]  Ludo M. G. M. Tolhuizen,et al.  On Perfect Ternary Constant Weight Codes , 1999, Des. Codes Cryptogr..