Additive cyclic codes over finite commutative chain rings

Download

index.pdf

Date

2018-07-01

Author

Martinez-Moro, Edgar
Otal, KAMİL
Özbudak, Ferruh

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

51
views

39
downloads

Additive cyclic codes over Galois rings were investigated in Cao et al. (2015). In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity. One of them is a natural generalization of the study in Cao et al. (2015), whereas the other one has some unusual properties especially while constructing dual codes. We interpret the reasons of such properties and illustrate our results giving concrete examples.

Subject Keywords

Theoretical Computer Science, Discrete Mathematics and Combinatorics

URI

https://hdl.handle.net/11511/38769

Journal

DISCRETE MATHEMATICS

DOI

https://doi.org/10.1016/j.disc.2018.03.016

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

On Lyapunov inequality in stability theory for Hill's equation on time scales Atici, FM; Guseinov, GS; Kaymakcalan, B (Springer Science and Business Media LLC, 2000-01-01) In this paper we obtain sufficient conditions for instability and stability to hold for second order linear Delta -differential equations on time scales with periodic coefficients.
On q-ary plateaued functions over F-q and their explicit characterizations Mesnager, Sihem; Özbudak, Ferruh; Sinak, Ahmet; Cohen, Gerard (Elsevier BV, 2019-08-01) Plateaued and bent functions play a significant role in cryptography, sequence theory, coding theory and combinatorics. In 1997, Coulter and Matthews redefined bent functions over any finite field F-q where q is a prime power, and established their properties. The objective of this work is to redefine the notion of plateaued functions over F-q, and to present several explicit characterizations of those functions. We first give, over F-q, the notion of q-ary plateaued functions, which relies on the concept o...
Invariant subspaces of collectively compact sets of linear operators Alpay, Safak; Misirlioglu, Tunc (Springer Science and Business Media LLC, 2008-01-01) In this paper, we first give some invariant subspace results for collectively compact sets of operators in connection with the joint spectral radius of these sets. We then prove that any collectively compact set M in alg Gamma satisfies Berger-Wang formula, where Gamma is a complete chain of subspaces of X.
Quivers of finite mutation type and skew-symmetric matrices Seven, Ahmet İrfan (Elsevier BV, 2010-11-01) Quivers of finite mutation type are certain directed graphs that first arised in Fomin-Zelevinsky's theory of cluster algebras. It has been observed that these quivers are also closely related with different areas of mathematics. In fact, main examples of finite mutation type quivers are the quivers associated with triangulations of surfaces. In this paper, we study structural properties of finite mutation type quivers in relation with the corresponding skew-symmetric matrices. We obtain a characterization ...
Mutation classes of finite type cluster algebras with principal coefficients Seven, Ahmet İrfan (Elsevier BV, 2013-06-15) Cluster algebras of finite type is a fundamental class of algebras whose classification is identical to the famous Cartan Killing classification. More recently, Fomin and Zelevinslcy introduced another central notion of cluster algebras with principal coefficients. These algebras are determined combinatorially by mutation classes of certain rectangular matrices. It was conjectured, by Fomin and Zelevinsky, that finite type cluster algebras with principal coefficients are characterized by the mutation classe...

Citation Formats

E. Martinez-Moro, K. Otal, and F. Özbudak, “Additive cyclic codes over finite commutative chain rings,” DISCRETE MATHEMATICS, pp. 1873–1884, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38769.