A New Family of Gold-like Sequences (Extended Abstract)
Khoongming Khoo, Guang Gong, Douglas R. Stinson · 2002
n 1 2 i=1 Tr(x 2 i +1 ) is Gold-like. In this pa- per, we generalise their concept and consider sequences represented by P n 1 2 i=1 ciTr(x 2 i +1 ),ci = 0,1 over GF(2 n ), n odd. Using techniques from linear algebra and cod- ing theory, we can eciently determine if the sequence is Gold-like by a polynomial gcd computation. Using the tools we developed, we prove that the sequence is Gold- like for all choice of coecients if and only if n is a prime of certain form. In the following, we first give the defini- tion of Gold-like sequences, then we proceed to the main result of this paper. Let GF(2 n ) be the finite field with 2 n elements and be a primitive element. Let f : GF(2 n ) ! GF(2). We say f(x) is the trace representation of the binary sequence a = {ai} 2 n 2 i=0 if ai = f( i ) for all i. Let m be the m-sequence represented by Tr(x). The cross correlation of a binary sequence a = {ai} 2 n 2 i=0 with m is