A quasi-symmetric 2-(49,9,6) design

Abstract: Huffman and Tonchev discovered four non-isomorphic quasi-symmetric 2-(49,9,6) designs. They arise from extremal self-dual [50,25,10] codes with a certain weight enumerator. In this note, a new quasi-symmetric 2-(49,9,6) design is constructed. This is established by finding a new extremal self-dual [50,25,10] code as a neighbor of one of the four extremal codes discovered by Huffman and Tonchev. A number of new extremal self-dual [50,25,10] codes with other weight enumerators are also found.