Multiplication by an Integer Constant: Lower Bounds on the Code Length

In this paper, we deal with code that performs a multiplication by a given integer constant using elementary operations, such as left shifts (i.e. multiplications by powers of two), additions and subtractions. Generating such a code can also be seen as a method to compress (or more generally encode) integers. We will discuss neither the way of generating code, nor the quality of this compression method, but this idea will here be used to find lower bounds on the code length, i.e. on the number of elementary operations. || Dans ce papier, nous parlons de code pour effectuer une multiplication par un entier donne a l'aide d'operations elementaires, comme des decalages vers la gauche (i.e. des multiplications par des puissances de deux), des additions et des soustractions. Ge