For an odd prime $ p and positive integers m \ell $, let \mathbb{F}_{p^m} be the finite field with p^{m} elements R_{\ell,m} = \mathbb{F}_{p^m}[v_1,v_2,\dots,v_{\ell}]/\langle v^{2}_{i}-1, v_{i}v_{j}-v_{j}v_{i}\rangle_{1\leq i, j\leq \ell} $. Thus is a commutative non-chain ring of order p^{2^{\ell} m} characteristic In this paper, we aim to construct quantum codes from skew constacyclic over F...

Let A be a ring with identity, id="M2"> σ endomorphism of id="M3"> that maps the identity to itself, id="M4"> δ id="M5"> -derivation id="M6"> , and consider skew-polynomial id="M7"> X ; , . When id="M8"> is ...

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...

In [4], starting from an automorphism θ of a finite field Fq and a skew polynomial ring R = Fq[X; θ], module θ-codes are defined as left R-submodules of R/Rf where f ∈ R. In [4] it is conjectured that an Euclidean self-dual module θ-code is a θ-constacyclic code and a proof is given in the special case when the order of θ divides the length of the code. In this paper we prove that this conjectu...

Let Fq be a finite field with q elements and denote by θ : Fq → Fq an automorphism of Fq. In this note, we deal with skew constacyclic codes, i.e. linear codes of Fnq which are invariant under the action of a semi-linear map T : Fnq → F n q , defined by T (a0, ..., an−2, an−1) := (αan−1, a0, ..., an−2) for some α ∈ Fq −{0} and n ≥ 2. In particular, we study some algebraic and geometric properti...

<p style='text-indent:20px;'>This paper is about a first characterization of LCD skew constacyclic codes and some constructions cyclic negacyclic over <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_{p^2} $\end{document}</tex-math></inline-formula>.</p>

Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 + u)-constacyclic codes over Z 4 + uZ 4 of any length are studied. A new Gray map between Z 4 + uZ 4 and Z 4 (4) is defined. By means of this map, it is shown that the Z 4 Gray image of a (1 + u)-constacyclic code of length n over ...