Design theory
Spreads in Strongly Regular Graphs
Designs, Codes and Cryptography - Special issue dedicated to Hanfried Lenz
The Search for Pseudo Orthogonal Latin Squares of OrderSix
Designs, Codes and Cryptography
Perfect Codes and Balanced Generalized Weighing Matrices
Finite Fields and Their Applications
Regular Hadamard Matrices Generating Infinite Families of Symmetric Designs
Designs, Codes and Cryptography
A recursive construction for new symmetric designs
Designs, Codes and Cryptography
Some implications on amorphic association schemes
Journal of Combinatorial Theory Series A
Recent progress in algebraic design theory
Finite Fields and Their Applications
| Hi-index | 0.00 |
A symmetric 2-(324, 153, 72) design is constructed that admits a tactical decomposition into 18 point and block classes of size 18 such that every point is in either 0 or 9 blocks from a given block class, and every block contains either 0 or 9 points from a given point class. This design is self-dual and yields a symmetric Hadamard matrix of order 324 of Bush type, being the first known example of a symmetric Bush-type Hadamard matrix of order 4n^2 for n 1 odd. Equivalently, the design yields a strongly regular graph with parameters v=324, k=153, \lambda=\mu=72 that admits a spread of cocliques of size 18. The Bush-type Hadamard matrix of order 324 leads to two new infinite classes of symmetric designs with parametersv=324(289^m+289^{m-1}+\cdots+289+1), \quad k=153(289)^m, \quad \lambda=72(289)^m,andv=324(361^m+361^{m-1}+\cdots+361+1), \quad k=171(361)^m, \quad \lambda=90(361)^m,where m is an arbitrary positive integer.