The algebraic decoding of the Z/sub 4/-linear Goethals code

The quaternary Goethals code is a Z/sub 4/-linear code of length 2/sup m/ which has 2(2/sup m+1)/(-3m-2) codewords and minimum Lee distance 8 for any odd integer m/spl ges/3. The Gray map of this code is known to be a nonlinear binary (2/sup m+1/, 2(2/sup m+1)/(-3m-2), 8) code. The covering radius of the Z/sub 4/-linear Goethals code is 6 and we present a complete decoding algorithm for the code.