In this letter, a block code that minimizes the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals is proposed. It is shown that peak envelope power is invariant to cyclic shift and codeword inversion. The systematic encoding rule for the proposed code is composed of searching for a seed codeword, shifting the register elements, and determining codeword inversion. This eliminates the look-up table for one-to-one correspondence between the source and the coded data. Computer simulation confirms that OFDM systems with the proposed code always have the minimum PAPR.