A new decoder for binary quadratic residue code with irreducible generator polynomial

The binary quadratic residue (QR) codes have nice distance property, but they are difficult to decode for the insufficient consecutive syndromes. The author used the Lagrange interpolation formula to calculate the needed primary unknown syndrome for the binary QR code. In this paper, we propose an efficient hardware architecture to implement this method, and decode the binary QR code by using the well-developed Berlekamp-Massey algorithm and Chien search.