Generalised Reed-Muller codes and power control in OFDM modulation

The power control problem in orthogonal frequency division multiplexing (OFDM) modulation is a notoriously difficult one. Here, we show how second order cosets of a q-ary generalisation of the first-order Reed-Muller code can be partitioned into Golay complementary sets, the size of the sets depending only on the quadratic form identifying the coset. This directly yields bounds on the peak to mean envelope power ratio (PMEPR) for OFDM codewords drawn from such cosets and leads to a family of high-rate OFDM codes which enjoy efficient encoding algorithms, useful error-correcting capability and tightly controlled PMEPR