Abstract
In this paper, we generalize the orthogonal double covers (ODC) of K-n,K-n as follows. The circular intensely orthogonal double cover design (CIODCD) of X = K-n,K-n,K-,K-,K-,K- n (sic) m is defined as a collection T = {G(00), G(10)... , G((n-1)0)} boolean OR {G(01), G(11),... , G((n-1)1)} of isomorphic spanning subgraphs of X such that every edge of X appears twice in the collection T, vertical bar E(G(i0))boolean AND E(G(j0))vertical bar = vertical bar E(G(i1))boolean AND E(G(j1))vertical bar = 0,i not equal jand vertical bar E(G(i0))boolean AND E(G(j1))vertical bar = lambda = ((m)(2)), i, j is an element of Z(n). We define the half starters and the symmetric starters matrices as constructing methods for the CIODCD of X. Then, we introduce some results as a direct application to the construction of CIODCD of X by the symmetric starters matrices.