Two methods for synthesizing generators of modulo codes with summation of weighted transitions with a sequence of weight coefficients, which forms a natural series of numbers are described. The first is based on the use of a cascade structure consisting of three blocks (activating the transition, weighing the activated transition and obtaining the weight of the information vector), and then optimizing the last two blocks. The second is related to the use of the same cascade structure, but with a selective approach to adding weighting factors in the third block and corresponding simplification of the second block - it only has a cascade of activating transitions between bits and a weighting factor. Both methods are universal and can be used to synthesize generators of other weighted codes with summation, including codes with summation of weighted information bits. For such codes with the information vector length m, the generators can be obtained by removing the cascade of activation of transitions in the code generator with summation of weighted transitions with the information vector length m + 1.