The only known circulant ordinary Hadamard matrix is developed from the initial row-1, 1, 1, 1. Letp be a prime, and letZp denote the cyclic group of orderp. In this paper, we construct circulantGH(p2;Zp) for all primesp. Whenp is odd, this result also extends the earlier result that there exist circulantGH(p;Zp) for all odd primesp. Other families ofGH-matrices which are developed modulo a group are discussed.
Early Result Cyclic Group Hadamard Matrix
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