Group permutable constant weight codes

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.