DOIAbstract
AbstractLet G be an abelian group of order g. A difference matrix based on G, denoted (g,k;1)-DM, is a k×g matrix A=[aij], aij in G, such that for each 1⩽r<s⩽k, the differences arj-asj, 1⩽j⩽g, comprise all the elements of G. If G=Zg, the difference matrix is called cyclic and denoted by (g,k;1)-CDM. Motivated by the construction of g-fan H(4,g,4,3), we consider the existence of (g,4;1)-DMs. It is proved that a (g,4;1)-DM exists if and only if g⩾4 and g≢2(mod4). Some new results on (g,k;1)-CDMs are also obtained, which are useful in the construction of both optical orthogonal codes and Z-cyclic whist tournaments
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