A note on constacyclic and skew constacyclic codes over the ring $\mathbb{Z}_{p} [u,v]/\langle u^2-u,v^2-v,uv-vu\rangle$
نویسندگان
چکیده
منابع مشابه
Skew constacyclic codes over Galois rings
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...
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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...
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Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right divisors of x − λ, where λ is a unit element, are exhibited. When λ = 1, the generators of Euclidean and Hermitian dual codes of such codes are determined tog...
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Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
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Article history: Received 13 February 2014 Accepted 18 April 2014 Available online 2 June 2014 Communicated by Gary L. Mullen
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ژورنال
عنوان ژورنال: Journal of Algebra Combinatorics Discrete Structures and Applications
سال: 2019
ISSN: 2148-838X
DOI: 10.13069/jacodesmath.617244