In this work, we study the DNA codes from the ring R = Z4 + wZ4, where w 2 = 2 + 2w with 16 elements. We establish a one to one correspondence between the elements of the ring R and all the DNA codewords of length 2 by defining a distance preserving Gau map φ. Using this map, we give several new classes of the DNA codes which satisfies reverse and reverse complement constraints. Some of the constructed DNA codes are optimal.
Fractional Repetition (FR) codes are well known class of Distributed Replication-based Simple Storage (Dress) codes for the Distributed Storage Systems (DSSs). In such systems, the replicas of data packets encoded by Maximum Distance Separable (MDS) code, are stored on distributed nodes. Most of the available constructions for the FR codes are based on combinatorial designs and Graph theory. In this work, we propose an elegant sequence based approach for the construction of the FR code. In particular, we propose a beautiful class of codes known as Flower codes and study its basic properties.
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