The algebraic decoding of the Z4-linear Goethals code

The quaternary Goethals code is a Z₄-linear code of length 2^m which has 2(2^m+1-3m-2) codewords and minimum Lee distance 8 for any odd m⩾3. The Gray map of this code is known to be a nonlinear binary (2^m+1, 2(2^m+1-3m-2), 8) code. The covering radius of the Z₄ -linear Goethals code is 6 and we present a complete decoding algorithm for the code