Good Code Sets via Coprime Powers

It is shown that a good code set with minimum peak cross-correlations (i.e.
$1/N$
in unity magnitude codes of length
$N$
) can be generated by replacing
$z$
, in any good code
$(c_N[n] \ \overset z{\Leftrightarrow} C_{N}(z))$
, by a set of coprime powers, each of which generates a member of the set. This is achieved by allowing only two elements of any two codes, one from each, in the set to meet at any relative delay within the correlation window. By beginning with a good code set, each of its members can be transformed into a good code set using the same coprime powers, resulting in a correspondingly larger good code set. All the codes are transmitted using the same frequency/channel. This approach of generating good code sets results in sparse codes. However, by spreading the generating code elements by any good code or members of a good code set, the average code efficiency can be significantly increased, while still keeping the average cross-correlation small. Such sets could be used in MIMO radar and orthogonal netted radar systems.