Construction of orthogonal starters and its consequences
Abstract
A method is proposed for constructing a system of (v−1)/2 pairwise disjoint orthogonal starters of order v for v ≡ 6k+1 ≡ 7 (mod 12) ≡ p ≡ (n2+n+1)/t such that the number 3 is one of the primitive roots of the Galois field of prime order p (k is prime, k ≠ 2, and n and t are positive integers). The starters occurring in this system satisfy certain additional conditions. The construction of a series of combinatorial structures, including some not previously known, is a consequence of this result.
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