IPM Positions

Non Resident Researcher (non-resident), School of Mathematics (2002 - 2003 )

Non IPM Affiliations

Assistant Professor of Shahid Rajaei University

Research Activities

A Hadamard matrix of order n is a square n by n matrix with entries in +1,-1 whose rows are pair wise orthogonal. Hadamard conjecture, which states that there exist Hadamard matrices of every order divisible by 4, has spawned a tremendous amount of research in combinatorial matrix theory, in the last century. Kharaghani and Kamali had generalized the concept of Golay sequences to the case where the entries are chosen from a signed group. By considering the dihedral group, we had introduced dihedral Golay sequences, and had obtained such sequences for lengths 7, 9, 15, and 19. These new sequences had been employed to produce complementary matrices. We had proved that by constructing Craigen - Geothals - Seidel array on these matrices, except for length 19, new classes of signed group Hadamard matrices are obtained. As a consequence, Hadamard matrices of a variety new orders had been produced. Now, the main problem is introducing a suitable array, to construct Hadamard matrices of new orders, by employing dihedral Golay sequences of length 19 and maybe other lengths

Present Research Project at IPM

Hadamard matrices

Related Papers

1.	H. Kharaghani, F. Kamali and G. B. Khosrovshahi Some Bush-type Hadamard matrices J. Statist. Plann. Inference 113 (2003), 375-384  [abstract]

2.	F. Kamali and H. Kharaghani Dihedral Golay sequences Australas. J. Combin. 139-145 (1998), 18  [abstract]