New algebraic decoding method for the (41, 21,9)‎ quadratic residue code

Abstract EN

In this paper, a decoding algorithm was given for the (41, 21, 9) binary QR code.

Here, some new more general prop retires are found for the syndromes of the subclass of binary QR codes of length n = 8l + 1.

Using these properties, the new theorems needed to decode this subclass of the QR codes are obtained and proved in [6].

For the binary (41, 21, 9) QR code, every known syndromes (resp., unknown syndromes) can be expressed as some power of S1 (resp., S3).

For the details about syndromes we refer the reader to [1].

A new algebraic decoding algorithm for the (41, 21, 9) binary QR code is pre sented.