A New Class of Orthogonal Designs

We give, among other results, a new method to construct for each positive integer \(n\) a class of orthogonal designs \( {OD}(4^{n+1};m;4^n m,4^n m,4^n m,4^n m)\), \(m=2^a 10^b 26^c +4^n+1\), \(a,b,c\) non-negative integers.