DNA Codes and Their Properties

One of the main research topics in DNA computing is associated with the design of information encoding single or double stranded DNA strands that are “suitable” for computation. Double stranded or partially double stranded DNA occurs as a result of binding between complementary DNA single strands (

A

is complementary to

T

and

C

is complementary to

G

). This paper continues the study of the algebraic properties of DNA word sets that ensure that certain undesirable bonds do not occur. We formalize and investigate such properties of sets of sequences, e.g., where no complement of a sequence is a prefix or suffix of another sequence or no complement of a concatenation of

n

sequences is a subword of the concatenation of

n

+ 1 sequences. The sets of code words that satisfy the above properties are called

θ

– prefix,

θ

-suffix and

θ

-intercode respectively, where

θ

is the formalization of the Watson-Crick complementarity. Lastly we develop certain methods of constructing such sets of DNA words with good properties and compute their informational entropy.