Orthomorphisms and the construction of projective planes

Spreads in Projective Hjelmslev Spaces over Finite Chain Rings

We prove a necessary and sufficient condition for the existence of spreads in the projective Hjelmslev geometries PHG Rn 1 R . Further, we give a construction of projective Hjelmslev planes from spreads that generalizes the familiar construction of projective planes from spreads in PG n q .

Families of optimal OOCs with λ = 2

We provide a new construction yielding one new and one known infinite family of optimal (n, w, 2)-optical orthogonal codes, w ∈ {4, 6}. Our construction relies on various techniques in finite projective spaces involving hyperovals in projective planes and Singer groups.

A new construction of self-dual codes from projective planes

The construction of self-dual binary codes from projective planes of odd order

Every finite projective plane of odd order has an associated self-dual binary code with parameters (2(q2 + q + q2 + q + 1, We also construct other related self-orthogonal and doubly-even codes, and the vectors of minimum weight. The weight enumerator polynomials for the planes of orders 3 and 5 are found. The boundary and coboundary maps are introduced.

Three families of multiple blocking sets in Desarguesian projective planes of even order

We present three families of multiple blocking sets in Desarguesian projective planes of even characteristic. The first and the third construction apply to any translation hyperoval. The second construction applies to arbitrary hyperovals. ∗The second and third authors were partially supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by th...