Linear DSP kernels such as transforms and filters are comprised exclusively of additions and multiplications by constants. These multiplications may be realized as networks of additions and wired shifts in hardware. The cost of such a "multiplierless" implementation is determined by the number of additions, which in turn depends on the value and precision of these constants. For a given transform or filter, the set of constants and their required precision is affected by algorithmic and implementation choices and hence provides a degree of freedom for optimization. In This work we present an automated method to generate, for a given linear transform, a minimum addition multiplierless implementation that satisfies a given quality constraint. The method combines automatic algorithm selection to improve numerical robustness and automatic search methods to minimize constant precisions in a chosen algorithm. We present experiments that show the trade-offs between cost and quality, including custom optimizations of the transforms used in JPEG image and MP3 audio decoders.