New construction of DNA codes with constant-GC contents from binary sequences with ideal autocorrelation

Abstract

In this paper, we provides a coding theoretic construction of DNA codes. Previously, some works have been carried out on DNA codes with biologically motivated constraints such as minimum Hamming distance and constant GC-content. Therefore, for given code-length N, the number of GC-content w, and minimum hamming distance d, it is interesting to construct DNA codes with maximum size A 4 GC (N, w, d). In the previous works, the DNA codes from the quaternary constant weight codes have been proposed [5]. In this paper, we propose another approach based on the binary constant weight codes, not quaternary ones. It is found that the size of the new DNA codes from binary constant weight codes is greater than or equal to that from the quaternary ones. First a general approach to constructing DNA codes from a binary constant weight code is proposed. Second, a specific DNA code with parameters (2n − 1, 2n−1, 2n−1) from binary sequences with ideal autocorrelation property is constructed.