A new family of Gold-like sequences
Khoongming Khoo, Guang Gong, Douglas R. Stinson · 2003
Families of sequences with low cross correlation have important applications in CDMA communications and cryptography. One class of such sequences are those which have period 2/sup n/-1 and cross correlation values -1, -1/spl plusmn/2 /sup (n+1)/2/ with m-sequence represented by Tr(x) when n is odd. These sequences are called Gold-like sequences and they are well studied in the literature, In this paper, we generalise their concept and consider sequences over GF(2/sup n/), n odd. Using techniques from linear algebra and coding theory, we can efficiently determine if the sequence is Gold-like by a polynomial gcd computation. Using the tools developed, we prove that the sequence is Gold-like for all choice of coefficients if and only if n is a prime of certain form.