Automorphisms and isomorphisms of Jha-Johnson semifields obtained from skew polynomial rings

We study the automorphisms of Jha-Johnson semifields obtained from an invariant irreducible twisted polynomial f ∈ K[t; σ], where K = Fq^n is a finite field and σ an automorphism of K of order n. We compute all automorphisms and some automorphism groups when f ∈ K[t; σ] has degree m and n ≥ m-1, in particular obtaining the automorphisms of Sandler and Hughes-Kleinfeld semifields. Partial results are obtained for n < m-1. We include the automorphisms of some Knuth semifields (which do not arise from skew polynomial rings).

Isomorphism between Jha-Johnson semifields are considered as well.


C. Brown < Christian.brown@nottingham.ac.uk >

S. Pumpluen < Susanne.pumpluen@nottingham.ac.uk >

A. Steele < andrew.steele@aquaq.co.uk >