Maximum likelihood soft decision decoding of linear block codes is addressed. A binary multiple-check generalization of the Wagner rule is presented, and two methods for its implementation, one of which resembles the suboptimal Forney-Chase algorithms, are described. Besides efficient soft decoding of small codes, the generalized rule enables utilization of subspaces of a wider variety than those recently applied (by Conway and Sloane, Be'ery and Snyders, and Forney) for coset decoding, thereby yielding maximum likelihood decoders with substantially reduced computational complexity for some larger binary codes. More sophisticated choice and exploitation of the structure of both a subspace and the coset representatives are demonstrated for the (24,12) Golay code, yielding a computational gain factor of about 2 with respect to previous methods. A ternary single-check version of the Wagner rule is applied for efficient soft decoding of the (12,6) ternary Golay code.