In this paper, we present two generators for the group of symmetries of the generic (m+1) -dimensional periodic Costas arrays over elementary abelian (\BBZp)mgroups: one that is defined by multiplication onmdimensions and the other by shear (addition) onmdimensions. Through exhaustive search, we observe that these two generators characterize the group of symmetries for the examples we were able to compute. Following the results, we conjecture that these generators characterize the group of symmetries of the generic (m+1) -dimensional periodic Costas arrays over elementary abelian (\BBZp)mgroups.

New families of three-dimensional (3-D) optical orthogonal codes for applications to optical code-division multiple access (OCDMA) networks are proposed. The families are based in the three dimensional periodic Welch Costas array over elementary Abelian groups. These new families are shown to be asymptotically optimal through the Johnson bound.

Improvements to the Johnson Bound for Optical Orthogonal Codes have been used to prove the optimality of double-periodic arrays with row and column length relatively prime. In our work we produce families of double-periodic arrays where the row and column length are not relatively prime. In this work we introduce the concept of group permutable constant weight codes and non-binary group permutable constant weight codes. We present improvements to the Johnson Bound to bound the cardinality of the families of double-periodic arrays whose row and column length are not relatively prime. We present some families of group permutable constant weight codes and prove the optimality of these families.

Yang and Fuja presented constructions of codes with unequal correlation constraints (lambdaca). And specifically they have constructions for the case where lambdaa= 2 > lambdac= 1. In their work they argue that it is important to make the cross-correlation (lambdac) as small as possible, and not necessarily lambdaa= lambdac. In this work we present a method to generate new Yang-Fuja type families with correlation constraints where lambdaca. We presented a method to increase the size of a family of a double periodic sequence with optical orthogonal code (OOC) length n = mp where m = p - 1, and p is a prime. In this work we present a new method that increases the size of a family of double periodic sequences without the restriction on m, we present a method to increase the weight of a double periodic array, and then combine both methods to produce Yang-Fuja type families of double periodic arrays with lambdaca. One of our main results is a theorem (Theorem 3, Section IV) that estimates lambdac. With this theorem we obtain two new constructions of optical orthogonal codes with lambdaca.