Some Notes on Prime-Square Sequences

The well-known binary Legendre sequences possess goodautocorrelation functions and high linear complexity, and are justspecial cases of much larger families of cyclotomic sequences.Prime-square sequences are the generalization of these Legendresequences, but the ratio of the linear complexity to the leastperiod of these sequences approximates to zero if the prime isinfinite. However, a relatively straightforward modification canradically improve this situation. The structure and properties,including linear complexity, minimal polynomial, and autocorrelationfunction, of these modified prime-square sequences are investigated.The hardware implementation is also considered.