We prove that semifield planes \pi(2m) coordinatized by the commutative binary Knuth semifield 2m, m=nk (m odd) are fractional dimensional with respect to a subplane isomorphic to PG(2, 4) if either n=9 or n \notequiv 0(mod 3) and one of the trinomials x^n+x^s+1, s \in {1, 2, 3, 5}, is irreducible over the Galois field 2.
Fractional dimension of binary Knuth semifield planes / O., Polverino; Trombetti, Rocco. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - 20:7(2012), pp. 317-327. [10.1002/jcd.20301]
Fractional dimension of binary Knuth semifield planes
TROMBETTI, ROCCO
2012
Abstract
We prove that semifield planes \pi(2m) coordinatized by the commutative binary Knuth semifield 2m, m=nk (m odd) are fractional dimensional with respect to a subplane isomorphic to PG(2, 4) if either n=9 or n \notequiv 0(mod 3) and one of the trinomials x^n+x^s+1, s \in {1, 2, 3, 5}, is irreducible over the Galois field 2.File in questo prodotto:
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