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Tanaka, Taichiro; Maruta, Tatsuya
Journal of geometry, 04/2014, Letnik: 105, Številka: 1Journal Article
A set K in PG( r , 4), r ≥ 2, is odd if every line meets K in an odd number of points. An odd set K in PG( r , 4), r ≥ 3, is FH-free if there is no plane meeting K in a Fano plane or in a non-singular Hermitian curve. We prove that an odd set K contains a hyperplane of PG( r , 4) if and only if K is FH-free. As an application to coding theory, a new extension theorem for quaternary linear codes is given.
