Let S be a blocking semioval in an arbitrary projective plane Π of order 9 which meets some line in 8 points. According to Dover in [2], 20 ≤ |S| ≤ 24. In [8] one of the authors showed that if Π is desarguesian, then 22 ≤ |S| ≤ 24. In this note all blocking semiovals with this property in all non-desarguesian projective planes of order 9 are completely determined. In any non-desarguesian plane Π it is shown that 21 ≤ |S| ≤ 24 and for each i ∈ {21, 22, 23, 24} there exist blocking semiovals of size i which meet some line in 8 points. Therefore, the Dover's bound is not sharp.

Abstract.We construct differentially 4-uniform functions over GF (2 n ) through Albert's finite commutative semifields, if n is even. The key observation there is that for some k with 0 ≤ k ≤ n − 1, the function

We proved affine planes corresponding to quadratic planar functions over F p n are semifield planes, and we determined affine planes corresponding to planar functions f (x) = x 10 − αx 6 − α 2 x 2 by Ding and Yuan. Moreover we calculated explicit shapes of planar functions from the square mappings of almost all known finite commutative semifields.

On strongly regular graphs with parameters (k, 0, 2) and their antipodal double coversNobuo NAKAGAWA

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