On Constant GC-content Cyclic DNA Codes With Long Codewords

In this study, we construct a cyclic DNA code that satisfies the Watson-Crick model, i.e., the reverse and the complement of any codeword are codewords. Similar to irreducible cyclic codes, we use the trace function over a finite field extension to generate our DNA code. MacWilliams-Seery algorithm to evaluate the weight distribution of binary irreducible cyclic codes is used to observe the GC-content distribution of our code. Then, a simple algorithm is proposed to select a sub-code with constant GC-content. Therefore, this sub-code would be a cyclic, reverse-complement, and constant GC-content DNA code. A few illustrative examples show the appropriateness of our algorithm for generating over 100000 DNA strands of length n > 1000 and a predefined constant GC-content.