Ternary codes, biplanes, and the nonexistence of some quasi-symmetric and quasi-3 designs
arXiv:2003.04453
Abstract
The dual codes of the ternary linear codes of the residual designs of biplanes on 56 points are used to prove the nonexistence of quasi-symmetric 2- and 2- designs with intersection numbers 0 and 3, and the nonexistence of a 2- quasi-3 design. The nonexistence of a 2- quasi-3 design is also proved.
9 pages, minor revision