A construction for binary sequence sets with low Peak-to-Average Power Ratio

Complementary Sequences (CS) have Peak-to-Average Power Ratio (PAR) less than or equal to 2 under the one-dimensional continuous Discrete Fourier Transform (DFT1infinity). Davis/Jedwab [1] constructed binary CS (DJ Set) for lengths 2(n) described by s = 2(-n/2)(-1)(p(x)), p(x) = Sigma(j=0)(L-2)x(pi(j+1))+c(j)x(j)+k, c(j), k is an element of Z(2). Hamming Distance, D, between sequences in this set satisfies D greater than or equal to 2(n-2). However the rate of the DJ set vanishes for n --> infinity, and higher rates are possible for PAR less than or equal to O(n) and D large. We present such a construction which generalises the DJ set. These codesets have PAR less than or equal to 2(t) under all Linear Unimodular Unitary Transforms (LUUTs), including all one and multi-dimensional continuous DFTs, and D greater than or equal to 2(n-d) where d is the maximum algebraic degree of the chosen subset of the complete set.