θ-Polycyclic Codes and θ-Sequential Codes over Finite Fields
نویسندگان
چکیده
In this paper we generalize the notion of cyclicity of codes, that is, θ-polycyclic codes and θ-sequential codes. It is shown that for a code C, C is θ-polycyclic (θ-sequential) if and only if its dual C⊥ is θ−1-sequential (θ−1-polycyclic). Furthermore, we study central θ-constacyclic codes. Mathematics Subject Classification: Primary 94B60; Secondary 94B15, 16W20
منابع مشابه
2-D skew constacyclic codes over R[x, y; ρ, θ]
For a finite field $mathbb{F}_q$, the bivariate skew polynomial ring $mathbb{F}_q[x,y;rho,theta]$ has been used to study codes cite{XH}. In this paper, we give some characterizations of the ring $R[x,y;rho,theta]$, where $R$ is a commutative ring. We investigate 2-D skew $(lambda_1,lambda_2)$-constacyclic codes in the ring $R[x,y;rho,theta]/langle x^l-lambda_1,y^s-lambda_2rangle_{mathit{l}}.$ A...
متن کاملA Note on The Enumeration of Euclidean Self-Dual Skew-Cyclic Codes over Finite Fields
In this paper, we give the enumeration formulas for Euclidean selfdual skew-cyclic codes over finite fields when (n, |θ|) = 1 and for some cases when (n, |θ|) > 1, where n is the length of the code and |θ| is the order of automorphism θ.
متن کاملA Note on the Existence of Self-Dual Skew Codes over Finite Fields
Conditions on the existence of self-dual θ-codes defined over a finite field IFq are studied for θ automorphism of IFq. When q ≡ 1 (mod 4) it is proven that there always exists a self-dual θ-code in any dimension and that self-dual θ-codes of a given dimension are either all θ-cyclic or all θ-negacyclic. When q ≡ 3 (mod 4), there does not exist a selfdual θ-cyclic code and a necessary and suffi...
متن کاملCoding with skew polynomial rings
In analogy to cyclic codes, we study linear codes over finite fields obtained from left ideals in a quotient ring of a (non commutative) skew polynomial ring. The paper shows how existence and properties of such codes are linked to arithmetic properties of skew polynomials. This class of codes is a generalization of the θ-cyclic codes discussed in [1]. However θ-cyclic codes are performant repr...
متن کاملA Note on the Dual Codes of Module Skew Codes
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...
متن کامل