On the Super Codes of the First Order Reed-Muller Code Based on m-Sequence Pairs

The super codes of the first order Reed-Muller code are widely used in the practical wireless communication systems, such as WCDMA and LTE. However, the super codes are usually obtained by exhaustive computer search, which involves huge computational cost. Therefore a systematic algorithm to construct the super codes beyond exhaustive computer search has been expected for long time. In this paper, we propose a systematic algorithm for the super codes construction base on the m-sequence pairs, which only involves some item permutation within the m-sequence. In addition, the constructed super codes outperform the conventional codes in terms of decoding error rate. Meanwhile, the super codes share the same characteristics as the conventional ones, such as being of arbitrary length and rate, and being efficiently decodable with Fast Hadamard Transform (FHT).