On algebraic decoding of the Z/sub 4/-linear Calderbank-McGuire code

The quaternary Calderbank-McGuire (see Des., Codes Cryptogr., vol.10, no.2, 1997) code is a Z/sub 4/-linear code of length 32 which has 2/sup 37/ codewords and a minimum Lee distance of 12. The Gray map of this code is known to be a nonlinear binary (64, 2/sup 37/,12) code. The Z/sub 4/-linear Calderbank-McGuire code can correct all errors with Lee weight /spl les/5. An algebraic decoding algorithm for the code is presented in this paper. Furthermore, we discuss an alternative decoding method which takes advantage of the efficient BCH decoding algorithm.