We analyze the lossless data compression scheme using antidictionary. Its principle is to build the dictionary of a set of words that do not occur in the text (minimal forbidden words). We prove here that the number of words in the antidictionary, i.e., minimum forbidden words, behaves asymptotically linearly in the length of the text under a memoryless model on the generation of texts. The linearity constant is explicited. We use methods from analytic combinatorics.