A majority decoding algorithm for a class of real-number codes is presented. Majority decoding has been a relatively simple and fast decoding technique for codes over finite fields. When applied to decode real-number codes, the robustness of the majority decoding to the presence of background noise, which is usually an annoying problem for existing decoding algorithms for real-number codes, is its most prominent property. The presented class of real-number codes has generator matrices similar to those of the binary Reed-Muller codes and is decoded by similar majority logic.

The utilization of real-number DFT codes for channel equalization is studied. As is shown, through real-number DFT codes, it is possible to deterministically calculate the dispersive parameters of a channel by introducing some redundancies into the transmitting data.>