5 research outputs found
An Algorithm for constructing Hjelmslev planes
Projective Hjelmslev planes and Affine Hjelmselv planes are generalisations
of projective planes and affine planes. We present an algorithm for
constructing a projective Hjelmslev planes and affine Hjelsmelv planes using
projective planes, affine planes and orthogonal arrays. We show that all
2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelsmelv
planes can be constructed in this way. As a corollary it is shown that all
2-uniform Affine Hjelmselv planes are sub-geometries of 2-uniform projective
Hjelmselv planes.Comment: 15 pages. Algebraic Design Theory and Hadamard matrices, 2014,
Springer Proceedings in Mathematics & Statistics 13
Three-weight codes over rings and strongly walk regular graphs
We construct strongly walk-regular graphs as coset graphs of the duals of
codes with three non-zero homogeneous weights over for
a prime, and more generally over chain rings of depth , and with a residue
field of size , a prime power. Infinite families of examples are built from
Kerdock and generalized Teichm\"uller codes. As a byproduct, we give an
alternative proof that the Kerdock code is nonlinear.Comment: 28 pages, 6 table