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Complementary sequences (CS) have peak-to-average power ratio (PAR) ≤ 2 under the one-dimensional continuous discrete Fourier transform (DFT1∞). Davis and Jedwab (see IEEE Trans. Inform. Theory, vol.45, no.7, p.2397-2417, 1999) constructed binary CS (DJ set) for lengths 2n described by s = 2-n2/ (-1)p(x), p(x) = Σj=0L-2xπ(j)xπ(j+1)+cjxj+k, cj, k ∈ Z2. Hamming distance, D, between sequences in this set satisfies D ≥ 2n-2. However the rate of the DJ set vanishes for n → ∞, and higher rates are possible for PAR ≤ O(n) and D large. We present such a construction which generalises the DJ set. These codesets have PAR ≤ 2t under all linear unimodular unitary transforms (LUUTs), including all one and multi-dimensional continuous DFTs, and D ≥ 2n-d where d is the maximum algebraic degree of the chosen subset of the complete set.