Linear and nonlinear constructions of DNA codes with Hamming distance d and constant GC-content

Coding theory has several applications in genetics and bioengineering. This paper constructs codes over an alphabet $\{$A,C,G,T$\}$ relevant to the design of synthetic DNA strands used in DNA microarrays, as DNA tags in chemical libraries and in DNA computing. The codes are designed to avoid unwanted hybridizations and to ensure uniform melting temperatures. Specifically, the codes considered here satisfy a Hamming distance constraint and a GC-content constraint. In comparison with previous work, longer codes are constructed, the examination of cyclic and extended cyclic codes is more comprehensive, attention is paid to the mapping from field or ring elements to $\{$A,C,G,T$\}$, cosets of codes are used and a nonlinear shortening operation is performed. Many new best codes are constructed, and are reproducible from the information presented here.