Decoding the (73, 37, 13) quadratic residue code

Abstract

Algebraic approaches to the decoding of the quadratic residue (QR) codes were studied recently. In Reed et. al. (1992), a decoding algorithm was given for the (41, 21, 9) binary QR code. Here, some new more general properties are found for the syndromes of the subclass of binary QR codes of length n = 8m +1. Using these properties, the new theorems needed to decode this subclass of the QR codes are obtained and proved. As an example of the application of these theorems, a new algebraic decoding algorithm for the (73, 37, 13) binary QR code is presented.