Mavron, Vassili C.; Jungnickel, D.; McDonough, Thomas(2001-11)

This paper establishes a correspondence between mutually orthogonal frequency squares (MOFS) and nets satisfying an extra property (“framed nets”). In particular, we provide a new proof for the bound on the maximal size ...

Key, Jennifer D.; McDonough, Thomas; Mavron, Vassili C.(2006-04)

We determine information sets for the generalized Reed–Muller codes and use these to apply partial permutation decoding to codes from finite geometries over prime fields. We also obtain new bases of minimum-weight vectors ...

Until recently, the known symmetric nets were class-regular and therefore satisfied a certain geometric condition that defines the class of nets known as tactical symmetric nets. Thus the known symmetric nets were tactical. ...

Mavron, Vassili C.; McDonough, Thomas; Schrikhande, M. S.(2003-03)

We show that a quasi-symmetric design with intersection numbers 1 and y > 1 and a good block belongs to one of three types: (a) it has the same parameters as PG 2(4, q), the design of points and planes in projective 4-space; ...

Key, Jennifer D.; McDonough, Thomas; Mavron, Vassili C.(2010-11-28)

We show that the first- and second-order Reed–Muller codes, and , can be used for permutation decoding by finding, within the translation group, (m−1)- and (m+1)-PD-sets for for m≥5,6, respectively, and (m−3)-PD-sets for ...