On image-difference matrices Original Research Article

Let G be an abelian group of order g. A difference matrix based on G, denoted image-DM, is a image matrix image, image in G, such that for each image, the differences image, image, comprise all the elements of G. If image, the difference matrix is called cyclic and denoted by image-CDM. Motivated by the construction of g-fan image, we consider the existence of image-DMs. It is proved that a image-DM exists if and only if image and image. Some new results on image-CDMs are also obtained, which are useful in the construction of both optical orthogonal codes and Z-cyclic whist tournaments.