Efficient Balanced and Maximum Homopolymer-Run Restricted Block Codes for DNA-Based Data Storage

We analyze codes for DNA-based data storage, which accounts for the maximum homopolymer repetition length and GC-AT balance. We present a new precoding method for translating words with a maximum run of k zeros into words with a maximum homopolymer run m = k+1, which is attractive for securing GC-AT balance. Generating functions are presented for enumerating the number of n-symbol k-constrained codewords of given GC-AT balance. Various efficient constructions are presented for block codes that satisfy a combined balance and maximum homopolymer run.