Algebraic decoding for classes of quantum codes

Overview & Synopsis

This paper describes a technique to perform the decoding of quantum Calderbank-Steane-Shor codes built from self-orthogonal classical binary codes possessing algebraic decoding procedures. This technique gives a viable alternative to syndrome decoding for codes with large minimum distance. The cases of Reed-Muller and BCH codes is examined. The new method is compared with syndrome decoding on illustrative examples. The asymptotic cost of both methods is also given.