Unitals and codes Original Research Article

A program is outlined for the enumeration of unital 2-(28,4,1) designs that uses tactical decompositions defined by vectors of certain weight in the dual binary code of a design. A class of designs with a spread that covers a codeword of weight 12 is studied in detail. A total of 909 nonisomorphic designs are constructed that include the classical hermitian and Ree unitals, as well as many other of the 145 previously known 2-(28,4,1) designs.