Double circulant self-dual codes using finite-field wavelet transforms

Abstract

This paper presents an example of integrating recently developed finite-field wavelet transforms into the study of error correcting codes. The primary goal of the paper is to demonstrate a straightforward approach to analyzing double circulant self-dual codes over any arbitrary finite-field using orthogonal filter bank structures. First, we discuss the proper combining of the cyclic mother wavelet and scaling sequence to satisfy the requirement of self-dual codes. Then as an example, we describe the encoder and decoder of a (12,6,4) self-dual code, and we demonstrate the simplicity and the computation reduction that the wavelet method offers for the encoding and decoding of this code. Finally, we give the mother wavelet and scaling sequence that generate the (24,12,8) Golay code.