Papers by Ahlem MELAKHESSOU
Journal of Applied Mathematics and Computing, May 11, 2017
In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-d... more In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring R = F q + vF q + v 2 F q , where v 3 = v, for q odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over R. Further, we give bounds on the minimum distance of LCD codes over F q and extend these to codes over R.
In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-d... more In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring R = F q + vF q + v 2 F q , where v 3 = v, for q odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over R. Further, we give bounds on the minimum distance of LCD codes over F q and extend these to codes over R.
arXiv (Cornell University), Apr 11, 2017
In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-d... more In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring R = F q + vF q + v 2 F q , where v 3 = v, for q odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over R. Further, we give bounds on the minimum distance of LCD codes over F q and extend these to codes over R.
In this paper, we study skew constacyclic codes over the ring ZqR where R = Zq + uZq, q = p s for... more In this paper, we study skew constacyclic codes over the ring ZqR where R = Zq + uZq, q = p s for a prime p and u2 = 0. We give the definition of these codes as subsets of the ring ZqR . Some structural properties of the skew polynomial ring R[x, θ] are discussed, where θ is an automorphism of R. We describe the generator polynomials of skew constacyclic codes over R and ZqR. Using Gray images of skew constacyclic codes over ZqR we obtained some new linear codes over Z4. Further, we have generalized these codes to double skew constacyclic codes over ZqR.
ArXiv, 2017
In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-d... more In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring $R=\F_{q}+v\F_{q}+v^{2}\F_{q}$, where $v^{3}=v$, for $q$ odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over $R$. Further, we give bounds on the minimum distance of LCD codes over $\F_q$ and extend these to codes over $R$.
Journal of Algebra Combinatorics Discrete Structures and Applications, 2020
In this paper, we study skew constacyclic codes over the ring $\mathbb{Z}_{q}R$ where $R=\mathbb{... more In this paper, we study skew constacyclic codes over the ring $\mathbb{Z}_{q}R$ where $R=\mathbb{Z}_{q}+u\mathbb{Z}_{q}$, $q=p^{s}$ for a prime $p$ and $u^{2}=0.$ We give the definition of these codes as subsets of the ring $\mathbb{Z}_{q}^{\alpha}R^{\beta}$. Some structural properties of the skew polynomial ring $ R[x,\Theta]$ are discussed, where $ \Theta$ is an automorphism of $R.$ We describe the generator polynomials of skew constacyclic codes over $\mathbb{Z}_{q}R,$ also we determine their minimal spanning sets and their sizes. Further, by using the Gray images of skew constacyclic codes over $\mathbb{Z}_{q}R$ we obtained some new linear codes over $\mathbb{Z}_{4}$. Finally, we have generalized these codes to double skew constacyclic codes over $\mathbb{Z}_{q}R$.
Journal of Applied Mathematics and Computing, 2017
In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-d... more In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring R = F q + vF q + v 2 F q , where v 3 = v, for q odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over R. Further, we give bounds on the minimum distance of LCD codes over F q and extend these to codes over R.
Journal of Algebra Combinatorics Discrete Structures and Applications
In this paper, we study skew constacyclic codes over the ring Z q R where R = Z q + uZ q , q = p ... more In this paper, we study skew constacyclic codes over the ring Z q R where R = Z q + uZ q , q = p s for a prime p and u 2 = 0. We give the definition of these codes as subsets of the ring Z α q R β. Some structural properties of the skew polynomial ring R[x, θ] are discussed, where θ is an automorphism of R. We describe the generator polynomials of skew constacyclic codes over R and Z q R. Using Gray images of skew constacyclic codes over Z q R we obtained some new linear codes over Z 4. Further, we have generalized these codes to double skew constacyclic codes over Z q R.
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Papers by Ahlem MELAKHESSOU