Legendre sequences for periodic non-coherent pulse compression

Perfect periodic cross-correlation is achievable in non-coherent pulse compression using Legendre sequences of any prime length. This paper briefly describes the (previously known) transmit and reference signals for the N = 4k − 1 case where N, the sequence length, is prime and k is a positive integer. It is then shown that a slight modification allows perfect periodic correlation with N = 4k − 3, doubling the number of available sequences.