The Constructions of DNA Codes from Linear Self-Dual Codes over Z4

Abstract

It is possible to construct DNA codes from classical linear codes. However, it is difficult to determine the GC weight enumerator. In this paper, we use the 4 Z -linear self-dual codes 4 m K to construct DNA codes. 4 m K have some good properties, so DNA codes can be easily constructed. Moreover, GC weight enumerator of the DNA codes can be easily determined. Keywords-self-dual codes; 4 Z codes; DNA codes I INTRODUCTION DNA is found naturally as a double stranded molecule, with a form similar to a twisted ladder. The backbone of the DNA helix is an alternating chain of sugars and phosphates, while the association between the two strands is variant combinations of the four nitrogenous bases adenine (A), thymine (T), guanine (G) and cytosine (C). The two ends of the strand are distinct and are conventionally denoted as 3' end and 5' end. Two strands of DNA can form (under suitable conditions) a double strand if the respective bases are Watson- Crick(1) complements of each other - A matches with T and C matches with G, also 3' end matches with 5' end. The problem of designing DNA codes (sets of words of fixed length n over the alphabets { } ,,, AC G T ) that satisfy certain combinatorial constraints has applications for reliably storing and retrieving information in synthetic DNA strands. These codes can be used in particular for DNA computing (2) or as molecular bar-codes. In this paper,we construct DNA codes from