Strong trinucleotide circular codes (Q666521)

Summary: In former papers we have identified a hierarchy relation between trinucleotide comma-free codes and trinucleotide circular codes [see Theor. Comput. Sci. 401, No. 1-3, 17--26 (2008; Zbl 1237.94043); Comput. Math. Appl. 55, No. 5, 989--996 (2008; Zbl 1195.92022)]. Here, we extend our hierarchy with two new classes of codes, called \(DLD\) and \(LDL\) codes, which are stronger than the comma-free codes. We also prove that no circular code with 20 trinucleotides is a \(DLD\) code and that a circular code with 20 trinucleotides is comma-free if and only if it is a \(LDL\) code. Finally, we point out the possible role of the symmetric group \(\sum_4\) in the mathematical study of trinucleotide circular codes.