DNA codes over two noncommutative rings of order four

DNA codes based on error-correcting codes have been successful in DNA-based computation and storage. Since there are four nucleobases in DNA, two well known algebraic structures such as the finite field $GF(4)$ and the integer modular ring $\mathbb{Z}_4$ have been used. However, due to various possibilities of DNA sequences, it is natural to ask whether there are other algebraic structures consisting of four elements. In this paper, we describe a new type of DNA codes over two noncommutative rings $E$ and $F$ of order four with characteristic 2. Our DNA codes are based on quasi self-dual codes over $E$ and $F$. Using quasi self-duality, we can describe fixed GC-content constraint weight distributions and reverse-complement constraint minimum distributions of those codes.