On the constructive enumeration of packings and coverings of index one
Discrete Mathematics - Combinatorial designs: a tribute to Haim Hanani
Isomorph-free exhaustive generation
Journal of Algorithms
Classification Algorithms for Codes and Designs (Algorithms and Computation in Mathematics)
Classification Algorithms for Codes and Designs (Algorithms and Computation in Mathematics)
Journal of Combinatorial Theory Series B
On the construction of polyharmonic B-splines
Journal of Computational and Applied Mathematics
The perfect binary one-error-correcting codes of length 15: part I-classification
IEEE Transactions on Information Theory
Upper bounds for constant-weight codes
IEEE Transactions on Information Theory
New code upper bounds from the Terwilliger algebra and semidefinite programming
IEEE Transactions on Information Theory
| Hi-index | 754.84 |
A binary code C ⊆ F2n with minimum distance at least d and codewords of Hamming weight w is called an (n, d, w) constant weight code. The maximum size of an (n, d, w). constant weight code is denoted by A(n, d, w), and codes of this size are said to be optimal. In a computer-aided approach, optimal (n, d, w) constant weight codes are here classified up to equivalence for d = 4, n ≤ 12; d = 6, n ≤ 14; d = 8, n ≤ 17; d = 10, n ≤ 20 (with one exception); d = 12, n ≤ 23; d = 14, n ≤ 26; d = 16, n ≤ 28; and d = 18, n ≤ 28. Moreover, several new upper bounds on A(n, d, w) are obtained, leading among other things to the exact values A(12, 4, 5) = 80, A(15, 6, 7) = 69, A(18, 8,7) = 33, A(19, 8, 7) = 52, A(19, 8, 8) = 78, and A(20, 8, 8) = 130. Since A(15, 6, 6) = 70, this gives the first known example of parameters for which A(n, d, w - 1) A(n, d, w) with w ≤ n/2. A scheme based on double counting is developed for validating the classification results.