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

摘要

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.