Fractional dimension of binary Knuth semifield planes |
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| Authors: | Olga Polverino Rocco Trombetti |
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| Institution: | 1. Dipartimento di Matematica, Seconda Università degli Studi di Napoli I-81100 Caserta, , Italy;2. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, , I-80126 Napoli, Italy |
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| Abstract: | We prove that semifield planes π(??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 ≡\ 0 ( mod 3 ) and one of the trinomials x n + x s + 1 , s ∈{ 1 , 2 , 3 , 5 }, is irreducible over the Galois field ?? 2 . © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 317–327, 2012 |
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| Keywords: | semifield semifield plane fractional dimensional plane |
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