Upper bounds for q-ary covering codes

New methods for constructing q-ary covering codes are presented. The author introduces the concepts of (p-) seminormal and strongly (p-) seminormal codes and shows how seminormal codes and punctured Hamming codes can be combined to construct new covering codes. Using these methods, upper bounds for ternary covering codes are improved. The new bounds are K/sub 3/

[1]  N. J. A. Sloane,et al.  Further results on the covering radius of codes , 1986, IEEE Trans. Inf. Theory.

[2]  Emile H. L. Aarts,et al.  New upper bounds for the football pool problem for 6, 7, and 8 matches , 1989, J. Comb. Theory, Ser. A.

[3]  Iiro S. Honkala,et al.  Modified bounds for coveting codes , 1991, IEEE Trans. Inf. Theory.

[4]  Patric R. J. Östergård,et al.  A new binary code of length 10 and covering radius 1 , 1991, IEEE Trans. Inf. Theory.

[5]  Wende Chen,et al.  New lower bounds for binary covering codes , 1988 .

[6]  N. J. A. Sloane,et al.  On a conjecture concerning coverings of Hamming space , 1984, AAECC.

[7]  Ewald W. Weber On the Football Pool Problem for 6 Matches: A New Upper Bound , 1983, J. Comb. Theory, Ser. A.

[8]  Iiro S. Honkala,et al.  Lower bounds for q-ary covering codes , 1990, IEEE Trans. Inf. Theory.

[9]  L. T. Wille The football pool problem for 6 matches: A new upper bound obtained by simulated annealing , 1987, J. Comb. Theory, Ser. A.

[10]  Heikki Hämäläinen,et al.  Upper bounds for football pool problems and mixed covering codes , 1991, J. Comb. Theory, Ser. A.

[11]  Lane A. Hemaspaandra,et al.  Using simulated annealing to design good codes , 1987, IEEE Trans. Inf. Theory.

[12]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[13]  R. G. Stanton,et al.  Covering Theorems for Vectors with Special Reference to the Case of Four and Five Components , 1969 .

[14]  Antoine Lobstein,et al.  On normal and subnormal q-ary codes , 1989, IEEE Trans. Inf. Theory.

[15]  Clement W. H. Lam,et al.  More Coverings by Rook Domains , 1984, J. Comb. Theory, Ser. A.

[16]  N. J. A. Sloane,et al.  On the covering radius of codes , 1985, IEEE Trans. Inf. Theory.