In Communication theory and Coding, it is expected that certain circulant matrices having k ones + 1 zeros in the first row are nonsingular. We prove such always nonsingular when 2 either a power of prime, or product two distinct primes. For any other integer we construct determinant 0. The smallest singular matrix appears = 45 . possibility for to be rather low, smaller than 10 − 4 this case.

In signal acquisition, Toeplitz and circulant matrices are widely used as sensing operators. They correspond to discrete convolutions and are easily or even naturally realized in various applications. For compressive sensing, recent work has used random Toeplitz and circulant sensing matrices and proved their efficiency in theory, by computer simulations, as well as through physical optical exp...

In this paper, we study norms of circulant matrices H = Circ(H 0 , H (k) 1 , . . . ,H (k) n−1) , H = Circ(H k , H (1) k , . . . ,H (n−1) k ) and r−circulant matrices Hr = Circr(H 0 ,H 1 , . . . ,H n−1) , Hr = Circr(H (0) k ,H (1) k , . . . ,H (n−1) k ) , where H (k) n denotes the n th hyperharmonic number of order r. Mathematics subject classification (2010): 15A60, 15B05, 11B99.

We employ theoretical and computational techniques to construct new weighing matrices constructed from two circulants. In particular, we construct W (148, 144), W (152, 144), W (156, 144) which are listed as open in the second edition of the Handbook of Combinatorial Designs. We also fill a missing entry in Strassler’s table with answer ”YES”, by constructing a circulant weighing matrix of orde...

In this paper, we study norms of circulant matrices F = Circ(F 0 , F (k) 1 , . . . ,F (k) n−1) , L = Circ(L 0 , L (k) 1 , . . . ,L (k) n−1) and r -circulant matrices Fr = Circr(F (k) 0 , F (k) 1 , . . . ,F (k) n−1) , Lr = Circr(L 0 , L (k) 1 , . . . ,L (k) n−1) , where F (k) n and L (k) n denote the hyper-Fibonacci and hyper-Lucas numbers, respectively. Mathematics subject classification (2010)...