arXiv subjects
Publications and source records attributed to Kenza Guenda.
This paper considers cyclic DNA codes of arbitrary length over the ring $R=\F_2[u]/u^4-1$. A mapping is given between the elements of $R$ and the alphabet $\{A,C,G,T\}$ which allows the additive stem distance to be extended to this ring. Cyclic codes over $R$ are designed such that their images under the mapping are also cyclic or quasi-cyclic of index 2. The additive distance and hybridization energy are functions of the neighborhood energy.
In this paper, we consider the construction of linear lexicodes over finite chain rings by using a $B$-ordering over these rings and a selection criterion. % and a greedy Algorithm. As examples we give lexicodes over $\mathbb{Z}_4$ and $\mathbb{F}_2+u\mathbb{F}_2$. %First, greedy algorithms are presented to construct %lexicodes using a multiplicative property. Then, greedy algorithms %are given for the case when the selection criteria is not %multiplicative such as the minimum distance constraint. It is shown that this construction produces many optimal codes over rings and also good binary codes. Some of these codes meet the Gilbert bound. We also obtain optimal self-dual codes, in particular the octacode.
For $λ$ an $n$-th power of a unit in a finite chain ring we prove that $λ$-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes. We also study the $α+p β$-constacyclic codes of length $p^s$ over the Galois ring $GR(p^e,r)$.
We give the structure of $λ$-constacyclic codes of length $p^sm$ over $R=\mathbb{F}_{p^r}+u \mathbb{F}_{p^r}+...+ u^{e-1}\mathbb{F}_{p^r}$ with $λ\in \F_{p^r}^*$. We also give the structure of $λ$-constacyclic codes of length $p^sm$ with $λ=α_1+uα_2+...+u^{e-1} α_{e-1}$, where $α_1,α_2 \neq 0$ and study the self-duality of these codes.
New infinite families of quantum symmetric and asymmetric codes are constructed. Several of these are MDS. The codes obtained are shown to have parameters which are better than previously known. A number of known codes are special cases of the codes given here.
In this paper we give the structure of constacyclic codes over formal power series and chain rings. We also present necessary and sufficient conditions on the existence of MDS codes over principal ideal rings. These results allow for the construction of infinite families of MDS self-dual codes over finite chain rings, formal power series and principal ideal rings.
We construct codes over the ring $\mathbb{F}_2+u\mathbb{F}_2$ with $u^2=0$. These code are designed for use in DNA computing applications. The codes obtained satisfy the reverse complement constraint, the $GC$ content constraint and avoid the secondary structure. they are derived from the cyclic complement reversible codes over the ring $\mathbb{F}_2+u\mathbb{F}_2$. We also construct an infinite family of BCH DNA codes.
In this paper we investigate repeated root cyclic and negacyclic codes of length $p^rm$ over $\mathbb{F}_{p^s}$ with $(m,p)=1$. In the case $p$ odd, we give necessary and sufficient conditions on the existence of negacyclic self-dual codes. When $m=2m'$ with $m'$ odd, we characterize the codes in terms of their generator polynomials. This provides simple conditions on the existence of self-dual negacyclic codes, and generalizes the results of Dinh \cite{dinh}. We also answer an open problem concerning the number of self-dual cyclic codes given by Jia et al. \cite{jia}.
We determine the permutation groups that arise as the automorphism groups of cyclic combinatorial objects. As special cases we classify the automorphism groups of cyclic codes. We also give the permutations by which two cyclic combinatorial objects on $p^m$ elements are equivalent.
We construct MDS Euclidean and Hermitian self-dual codes over large finite fields of odd and even characteristics. Our codes arise from cyclic and negacyclic duadic codes.
We give the class of finite groups which arise as the permutation groups of cyclic codes over finite fields. Furthermore, we extend the results of Brand and Huffman et al. and we find the properties of the set of permutations by which two cyclic codes of length p^r can be equivalent. We also find the set of permutations by which two quasi-cyclic codes can be equivalent.
We characterize the affine-invariant maximal extended cyclic codes. Then by the CSS construction, we derive from these codes a family of pure quantum codes. Also for ordnq even, a new family of degenerate quantum stabilizer codes is derived from the classical duadic codes. This answer an open problem asked by Aly et al.