Linear Span of the Optimal Frequency Hopping Sequences from Irreducible Cyclic Codes

Optimal set of the frequency hopping sequences can be derived from some irreducible cyclic codes. This paper determines the linear span of the frequency hopping sequences in the optimal set. The linear span is much less than the length of the frequency hopping sequences. In order to improve the linear span, we use two types of permutation polynomials, power permutation and binomial permutation, to transform the optimal set of the frequency hopping sequences. The transformed frequency hopping sequences have optimal Hamming correlation and larger linear span than the original frequency hopping sequences. Compared with the original frequency hopping sequences, the transformed optimal frequency hopping sequences have higher security to resist the cryptanalytic method.