Testing Whether a Set of Code Words Satisfies a Given Set of Constraints

This paper investigates the problem of testing whether a set of code words satisfies certain biologically motivated Hamming distance constraints. The paper provides three efficient techniques to verify the code words, namely, the Enumeration, Table Lookup, and Encoding methods, with applications to the design of DNA words. The Enumeration method enumerates all combinations of positions in a word, so that all the words in a set can be compared simultaneously and the testing process is improved. The Table Lookup method constructs a data table and divide each word into sub-words to reduce the time complexity of the testing process. The Encoding method which is similar to Table Lookup method uses a linked list to store necessary information in addition. The proposed methods run in O(n) ~ O(log log n) times faster than the naive method when = O(log n), where n is the number of code words in a set and is the length of a word.