Upper bound on one-coincidence sequences of odd length with distance constraints in frequency-hopping spread-spectrum systems

We deal with one-coincidence sequences for the frequency-hopping CDMA systems. We derive an upper bound on the number of one-coincidence sequences of odd length where the distances between all adjacent frequency indices are required to be greater than a specified distance value. It is shown that there exist infinitely many cases in which our bound is tighter than the conventional bound.