On reversibility problem in DNA bases over a class of rings

Abstract

Let [Formula: see text] be a non-chain ring of characteristic 4, where [Formula: see text] and [Formula: see text]. In this article, we discuss reversible cyclic codes of odd lengths over the ring [Formula: see text]. We construct bijections between the elements of the ring [Formula: see text] and DNA-[Formula: see text] bases for k = 1, 2 in such a manner that the reversibility problem is solved. Employing these bijections, reversible complement cyclic codes of odd lengths are generated. Furthermore, we construct a Gray map [Formula: see text] and as an application of the Gray map Φ, we obtain the GC-content of cyclic codes of arbitrary odd length over the ring [Formula: see text]. Meanwhile, we provide some examples of reversible cyclic codes of odd lengths over the ring [Formula: see text] for different values of k, and also obtain the Lee distances of these codes.

Keywords

• Cyclic codes
• reversible codes
• DNA codes
• GC-content
• 94B05
• 94B15