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We present a new construction of 16-QAM Golay sequences of length n = 2m. The number of constructed sequences is (14 + 12m)(m!/2)4m+1. When employed as a code in an orthogonal frequency-division multiplexing (OFDM) system; this set of sequences has a peak-to-mean envelope power ratio (PMEPR) of 3.6. By considering two specific subsets of these sequences, we obtain new codes with PMEPR bounds of 2.0 and 2.8 and respective code sizes of (2 + 2m)(m!/2)4m+1 and (4 + 4m)(m!/2)4m+1. These are larger than previously known codes for the same PMEPR bounds.