Periodic ambiguity functions of EQC-based TFHC

The time-frequency hop codes based upon extended quadratic congruences (TFHC-EQC) were developed previously (1988, 1991). The known results about the ambiguity functions of the TFHC-EQC are extended from aperiodic cases to periodic cases. Precisely, the following new results are proved: (1) The tight upper bound for the periodic auto-ambiguity function of the TFHC-EQC is 6; (2) the periodic cross-ambiguity upper bound of the TFHC-EQC is at least (N-1)/2; (3) there exists a subset TFHC-EQC of volume (N-1)/2 such that its periodic cross-ambiguity is tightly upper bounded by 8.