منابع مشابه
$\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})$-Linear Skew Constacyclic Codes
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 ...
متن کاملOn Codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$
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 ove...
متن کاملSkew cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$
In this article, we study skew cyclic codes over ring R = Fq + vFq + v 2 Fq, where q = p, p is an odd prime and v3 = v. We describe generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over R by a decomposition theorem. We also describe the generator polynomials of the duals of skew cyclic codes. Moreover, the idempotent genera...
متن کاملThe Dual and the Gray Image of Codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$
v Fq and their Gray images, where v 3 = v. We define the Lee weight of the elements of R, we give a Gray map from R to F 3n q and we give the relation between the dual and the Gray image of a code. This allows us to investigate the structure and properties of self-dual cyclic, formally self-dual and the Gray image of formally self-dual codes over R. Further, we give several constructions of for...
متن کاملA new trace bilinear form on cyclic $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes
Let Fq be a finite field of cardinality q, where q is a power of a prime number p, t ≥ 2 an even number satisfying t 6≡ 1 (mod p) and Fqt an extension field of Fq with degree t. First, a new trace bilinear form on F n qt which is called ∆-bilinear form is given, where n is a positive integer coprime to q. Then according to this new trace bilinear form, bases and enumeration of cyclic ∆-self-ort...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2003
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2003.v10.n2.a8