N-orthogonal phase-modulated codes

In this paper biorthogonal codes are generalized in a natural way to a class of codes, called
N
-orthogonal codes.
N
-orthogonal codes consist of
N^{M}
signals divided into
N^{M-1}
disjoint sets of
N
signals where signals in different sets are uncorrelated or orthogonal. One instance of the
N
-orthogonal codes is realized as a class of polyphase, constant-power modulated signals, the admissible phase set being denoted by
N^{th}
roots of unity. Matched filter receiver criteria for the Gaussian channel are developed and simplified integral expressions for the probability of error are derived.