This paper is dealing with DNA cyclic codes which play an important role in DNA computing and have attracted a particular attention in the literature. Firstly, we introduce a new family of DNA cyclic codes over the ring R = F2[u]/(u ). Such codes have theoretical advantages as well as several applications in DNA computing. A direct link between the elements of such a ring and the 64 codons used...

Abstract In 2010, Rhoades proved that promotion on rectangular standard Young tableaux, together with the associated fake-degree polynomial, provides an instance of cyclic sieving phenomenon. We extend this result to m -tuples skew tableaux same shape, for fixed , subject condition th power polynomial evaluates nonnegative integers at roots unity. However, we are unable specify explicit group a...

Let D2n = 〈x, y | x = 1, y = 1, yxy = x〉 be a dihedral group, and R = GR(p, m) be a Galois ring of characteristic p and cardinality p where p is a prime. Left ideals of the group ring R[D2n] are called left dihedral codes over R of length 2n, and abbreviated as left D2n-codes over R. Let gcd(n, p) = 1 in this paper. Then any left D2n-code over R is uniquely decomposed into a direct sum of conca...

The totalistic two-dimensional cellular automaton code 52 is capable of a wide variety of behavior. In this paper we look at its generic behavior, its complex behavior on simple backgrounds, its versatility in performing finite computations, and its block emulations of elementary cellular automata (ECA). In all, we found 65 ECA which are emulated by code 52. Taken together, the evidence is stro...

An n-bit (cyclic) Gray code is a (cyclic) sequence of all n-bit strings such that consecutive strings differ in a single bit. We describe an algorithm which for every positive integer n constructs an n-bit cyclic Gray code whose graph of transitions is the d-dimensional hypercube Qd if n = 2, or a subgraph of Qd if 2 d−1 < n < 2. This allows to compress sequences that follow this code so that o...

We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied. As an application, skew constacyclic self-dual codes over GR(4) are constr...

A (left) group code of length n is a linear code which is the image of a (left) ideal of a group algebra via an isomorphism FG→ F which maps G to the standard basis of F. Many classical linear codes have been shown to be group codes. In this paper we obtain a criterion to decide when a linear code is a group code in terms of its intrinsical properties in the ambient space F, which does not assu...