Hadamard matrices of generalized quaternion type

Jacket matrices constructed from Hadamard matrices and generalized Hadamard matrices

Quasi-Cyclic Generalized Hadamard Matrices

In this paper, we define quasi-cyclic(QC) generalized Hadamard matrices and balanced QC generalized Hadamard matrices. Then we propose a new construction method for QC generalized Hadamard matrices. The proposed matrices are constructed from the balanced optimal low correlation zone(LCZ) sequence set which has correlation value −1 within low correlation zone.

Expanding generalized Hadamard matrices over Gm by substituting several generalized Hadamard matrices over G

Over an additive abelian group of order and for a given positive integer , a generalized Hadamard matrix is defined as a matrix , where and , such that every element of appears exactly times in the list , , , , for any . In this paper, we propose a new method of expanding a over by replacing each of its -tuple with where . We may use (not necessarily all distinct) ’s for the substitution and th...

On generalized Hadamard matrices of minimum rank

Generalized Hadamard matrices of order qn−1 (q a prime power, n ≥ 2) over GF (q) are related to symmetric nets in affine 2-(qn, qn−1, (qn−1 − 1)/(q − 1)) designs invariant under an elementary abelian group of order q acting semi-regularly on points and blocks. The rank of any such matrix over GF (q) is greater than or equal to n− 1. It is proved that a matrix of minimum q-rank is unique up to a...

On Classification of Generalized Hadamard Matrices

In this paper, we give an algorithm to list and classify generalized Hadamard matrices of a given order over an arbitrary elementary Abelian group. Generalized Hadamard matrices of order less than or equal to 16 over Abelian groups Z3; Z4, Z2 Z2 and Z5 have been classi…ed up to equivalence. We have shown that generalized Hadamard matrices of order 4; 8, and 12 over EA(4) are unique up to equiva...