Number of frequency slots in low collision Reed Solomon based frequency hopping sequences

Abstract

The idea of relating cyclic codes and frequency hopping (FH) sequences has yielded families of FH sequences, which meet tight bounds. Reed Solomon based FH sequences are an instance of such families. In this paper, these sequences are investigated for Galois fields of characteristic two. More specifically, the symbols utilized in each of sequences are calculated for two important cases, where hamming correlation between sequences is at most three. It has been shown that regardless of the length of sequence, the number of symbols utilized in such sequences can take only 5 values, and there is no sequence in which other number of symbols are used. The number of sequences in which a specified number of symbols are used is also counted, which shows that there is significant variation between the numbers of sequences as the number of symbols changes.