The Study Of DNA Codes On A Class Of Rings

Since the 1970s,research on algebraic coding theory has made great progress and has been widely used in practice.With the development of algebraic coding theory,more and more scholars at home and abroad have paid attention to the research of coding theory on the finite rings.The codes on the finite rings are combined with the DNA sequence to obtain a new type of codes.DNA computing began in 1994,It has more excellent properties than traditional computing methods.Since DNA computing can store more memory than silicon based computing systems,DNA has a very good error detecting and hence correcting capability.To make DNA computing more reliable in information transmission,it is necessary to effectively encode information,so researchers combined the excellent characteristics of DNA with the code on the ring to obtain the DNA code.By combining of the algebraic structure of rings and DNA sequences and using the biological characteristics of DNA molecules,a one-to-one correspondence between the sequence on rings and the set of bases in DNA is constructed.A more sophisticated encoding method is obtained.This method has the characteristics of high efficiency,low error rate,small redundancy and high code rate in decoding.In this paper,the mapping between the cyclic code on the finite ring F4[u]/<u3-1>and the DNA base sequence is established.Combining the good biological characteristics of the DNA sequence with the algebraic nature of the finite rings,some DNA cyclic codes are obtained.The necessary and sufficient conditions for the reversible-complement DNA codes on the ring are given.Furthermore,a feasible method to construct DNA cyclic codes on F4[u]/<uk-1>,which breaks through the limitation of the traditional method of constructing cyclic codes on rings F4[u]/<u3-1>.Some concrete examples are given to verify the feasibility of this method.