✦ LIBER ✦
Fractional dimension of binary Knuth semifield planes
✍ Scribed by Olga Polverino; Rocco Trombetti
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 147 KB
- Volume
- 20
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We prove that semifield planes π(𝕂~2__m__~) coordinatized by the commutative binary Knuth semifield 𝕂~2__m__~, 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 𝔽~2~. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 317–327, 2012