Modified Jacobi sequences

Quadratic residue and tw in prime sequences are well known types of binary sequence with ideal periodic autocorrelation functions. These are just spec ial cases of much larger families of sequences referred to here as Legendre sequences and modified Jacobi sequences. Although these more general forms are suboptimal and do not have ideal autocorrelation functions, neverthele ss they do exhibit out-of-phase autocorrelation values which are independen t of their lengths, and so the longer sequences may be useful. The structur e and properties of these sequences are investigated, and a two-dimensional array representation that enables the sequences and their autocorrelation functions to be derived in a simple and compact manner are employed.