CLASSES OF FORMS WITT EQUIVALENT TO A SECOND TRACE FORM OVER FIELDS OF CHARACTERISTIC TWO

Invariants of trace forms over finite fields of characteristic 2

Let K be a finite extension of F2. We compute the invariants of the quadratic form Q(x) = trK/F2(x(x 2a + x2 b )) and so determine the number of zeros in K. This is applied to finding the cross-correlation of certain binary sequences. Set F = F2 and K = F2k . Let

Quadratic Forms over Fields Ii: Structure of the Witt Ring

On hermitian trace forms over hilbertian fields

Let k be a field of characteristic different from 2. Let E/k be a finite separable extension with a k-linear involution σ. For every σ-symmetric element μ ∈ E∗, we define a hermitian scaled trace form by x ∈ E 7→ TrE/k(μxx). If μ = 1, it is called a hermitian trace form. In the following, we show that every even-dimensional quadratic form over a hilbertian field, which is not isomorphic to the ...

Trace forms over finite fields of characteristic 2 with prescribed invariants

Set F = F2 and K = F2k . Let

HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC

Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...