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...

<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>

Generalizing even-like duadic cyclic codes and Type-II duadic negacyclic codes, we introduce even-like (i.e.,Type-II) and odd-like duadic constacyclic codes, and study their properties and existence. We show that even-like duadic constacyclic codes are isometrically orthogonal, and the duals of even-like duadic constacyclic codes are odd-like duadic constacyclic codes. We exhibit necessary and ...

We consider the algorithmic problem of computing a primitive idempotent central simple algebra over field rational functions finite field. The is given by set structure constants. reduced to computation division Brauer equivalent algebra. This constructed as cyclic algebra, once Hasse invariants have been computed. give an application skew constacyclic convolutional codes.