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 quasi-symmetric designs with these parameters. The parameters belong to the families 2 - (2u(2) - u,u (2) -u,u(2) - u - 1) and 2 - (2u(2) + u,u(2), u(2) - u), which are related to Hadamard parameters. The designs correspond to new codes meeting the Grey-Rankin bound.
quasi-symmetric mutually orthogonal latin squares grey-rankin bound binary code hadamard matrix