A bound on correlation immunity.
A class of latin squares derived from finite abelian groups
We consider two classes of latin squares that are prolongations of Cayley tables of finite abelian groups. We will show that all squares in the first of these classes are confirmed bachelor squares, squares that have no orthogonal mate and contain at least one cell though which no transversal passes, while none of the squares in the second class can be included in any set of three mutually orthogonal latin squares.
A construction method for complete sets of mutually orthogonal frequency squares.
A construction method for generalized Room squares.
A construction method for generalized Room squares. (Short Communication).
A generalization of transversals for Latin squares.
A Recursive Construction for Room Designs
A regular graph of girth 6 and valency 11.
A uniqueness result for -homogeneous latin trades
A latin trade is a subset of a latin square which may be replaced with a disjoint mate to obtain a new latin square. A -homogeneous latin trade is one which intersects each row, each column and each entry of the latin square either or times. In this paper, we show that a construction given by Cavenagh, Donovan and Drápal for -homogeneous latin trades in fact classifies every minimal -homogeneous latin trade. We in turn classify all -homogeneous latin trades. A corollary is that any -homogeneous...
Algebraic and Combinatorial Characterization of Latin squares I
Algorithm for the complement of orthogonal operations
G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a -tuple of orthogonal -ary operations, where , to an -tuple of orthogonal -ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a -tuple of orthogonal -ary operations to an -tuple of orthogonal -ary operations and an algorithm for complementing a -tuple of orthogonal -ary operations to an -tuple of orthogonal -ary operations. Also we find some...
An even side analogue of Room squares.
Atomic Latin squares based on cyclotomic orthomorphisms.
Biembeddings of symmetric configurations and 3-homogeneous Latin trades
Using results of Altshuler and Negami, we present a classification of biembeddings of symmetric configurations of triples in the torus or Klein bottle. We also give an alternative proof of the structure of 3-homogeneous Latin trades.
Commutative subloop-free loops
We describe, in a constructive way, a family of commutative loops of odd order, , which have no nontrivial subloops and whose multiplication group is isomorphic to the alternating group .
Completing partial Latin squares with two filled rows and two filled columns.
Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results
We review results for the embedding of orthogonal partial Latin squares in orthogonal Latin squares, comparing and contrasting these with results for embedding partial Latin squares in Latin squares. We also present a new construction that uses the existence of a set of mutually orthogonal Latin squares of order to construct a set of mutually orthogonal Latin squares of order .
Construction of a net without transversals over a non-planar near-field
Construction of quasigroups having a large number of orthogonal mates
Construction of the mutually orthogonal extraordinary supersquares
Our purpose is to determine the complete set of mutually orthogonal squares of order d, which are not necessary Latin. In this article, we introduce the concept of supersquare of order d, which is defined with the help of its generating subgroup in . We present a method of construction of the mutually orthogonal supersquares. Further, we investigate the orthogonality of extraordinary supersquares, a special family of squares, whose generating subgroups are extraordinary. The extraordinary subgroups...