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Ternary codes, biplanes, and the nonexistence of some quasisymmetric and quasi‐3 designs
Author(s) -
Munemasa Akihiro,
Tonchev Vladimir D.
Publication year - 2020
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21740
Subject(s) - mathematics , ternary operation , intersection (aeronautics) , combinatorics , residual , discrete mathematics , algorithm , computer science , engineering , programming language , aerospace engineering
The dual codes of the ternary linear codes of the residual designs of biplanes on 56 points are used to prove the nonexistence of quasisymmetric 2‐ ( 56 , 12 , 9 ) and 2‐ ( 57 , 12 , 11 ) designs with intersection numbers 0 and 3, and the nonexistence of a 2‐ ( 267 , 57 , 12 ) quasi‐3 design. The nonexistence of a 2‐ ( 149 , 37 , 9 ) quasi‐3 design is also proved.