ABSTRACT
In this chapter, we describe a model for spreads based on the work of Oyama [1079]. Let V2n be a 2n-dimensional vector space over GF (q). Then a spread of V2n is, of course, a set of q
n + 1 mutually disjoint n-dimensional GF (q)-subspaces. Choose a basis and represent vectors in V2n as 2n-tuples (x1, x2, . . . , xn, y1, y2, . . . , yn), xi, yi ∈ GF (q). The idea is to consider GF (q
n)×GF (qn) as V2n and find a suitable representation for spreads. Basically, this is set up so that for x ∈ GF (qn), we consider the n-tuple
(x, xq, xq 2
, xq 3
, . . . , xq n−1
) = [x],
so that for x, y ∈ GF (qn), ([x], [y]) will represent our 2n-vector over GF (q). Let
ω =
0 . . . . 0 1 1 0 . . . . 0 0 1 . . . . 0 . 0 1 . . . 0 . . 0 1 . . . . . . . . . . 0 . . . . 1 0
.
