DCA (Data Compression using Antidictionaries) is a novel lossless data compression method working on bit streams presented by Crochemore et al. DCA takes advantage of words that do not occur as factors in the text, i.e. that are forbidden. Due to these forbidden words (antiwords), some symbols in the text can be predicted. We build the antidictionary using suffix array in time O(k * N log N), where k is maximal antiword length. Length of suffix array and LCP constructed over the binary alphabet will be 8 times length of the input text. Still memory requirements for suffix array and LCP construction depend only on the length N of input text with O(N), instead of suffix trie with exponential complexity.