A new family of Gold-like sequences

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 2ⁿ-1 and cross correlation values -1, -1±2 ⁽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(2ⁿ), 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.