New quasi-symmetric designs constructed using mutually orthogonal Latin squares and Hadamard matrices

Using Hadamard matrices and mutually orthogonal Latin squares, we construct two new quasi-symmetric designs, with parameters 2 (66, 30, 29) and 2 - (78, 36, 30). These are the first examples of quasisymmetric designs with these parameters. The parameters belong to the families 2-(2u2 -u, u2 -u, u2 -u-1) and 2-(2u2 +u, u2, u2 -u) which are related to Hadamard parameters. The designs correspond to new codes meeting the Grey-Rankin bound.

• Type: Conference
• Year: 2006
• Where: DCC
• Authors: Carl Bracken, Gary McGuire, Harold N. Ward
• Keywords: Computer Graphics, DCC 2006, Hadamard Matrices, Orthogonal Latin Squares