This paper presents two new maximum likelihood decoding (MLD) algorithms for linear codes over Z-channel, which are much more efficient than conventional exhaustive algorithms for high rate codes. In the proposed algorithms, their complexities are reduced by employing the projecting set Cs of the code, which is determined by the "projecting" structure of the code. Space and computational complexities of algorithms mainly depend upon the size of Cs which is usually several times smaller than the total number of codewords. It is shown that the upper bounds on computational complexities of decoding algorithms are in proportion to the number of parity bits and the distance between an initial estimate of the codeword and the received word, respectively, while space complexities of them are equal to the size of Cs. Lastly, numerical examples clarify the average computational complexities of the proposed algorithms, and the efficiency of these algorithms for high rate codes is confirmed.