On a class of repeated root monomial like abelian codes

Download

index.pdf

Date

2015-04-01

Author

Martinez Moro, Edgar
Özadam, Hakan
Özbudak, Ferruh
szabo, steve

Metadata

Show full item record

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

Item Usage Stats

136
views

67
downloads

In this paper we study polycyclic codes of length p s 1 × ⋯ × p s n p s 1 ×⋯×p s n \ over $\F_{p^a}$\ generated by a single monomial. These codes form a special class of abelian codes. We show that these codes arise from the product of certain single variable codes and we determine their minimum Hamming distance. Finally we extend the results of Massey et. al. in \cite{MASSEY_1973} on the weight retaining property of monomials in one variable to the weight retaining property of monomials in several variables.

Subject Keywords

Repeated-root Cyclic code, Abelian code, Weight-retaining property

URI

https://hdl.handle.net/11511/42513
https://jacodesmath.com/index.php/jacodesmath/article/view/13

Journal

Journal of Algebra Combinatorics Discrete Structures and Applications

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

ON THE k-TH ORDER LFSR SEQUENCE WITH PUBLIC KEY CRYPTOSYSTEMS KIRLAR, Barış Bülent; Cil, Melek (Walter de Gruyter GmbH, 2017-06-01) In this paper, we propose a novel encryption scheme based on the concepts of the commutative law of the k-th order linear recurrences over the finite field F-q for k > 2. The proposed encryption scheme is an ephemeral-static, which is useful in situations like email where the recipient may not be online. The security of the proposed encryption scheme depends on the difficulty of solving some Linear Feedback Shift Register (LFSR) problems. It has also the property of semantic security. For k = 2, we propose ...
Construction of self dual codes from graphs Fellah, Nazahet; Guenda, Kenza; Özbudak, Ferruh; Seneviratne, Padmapani (2022-07-01) In this work we define and study binary codes C-q,C-k and (C-q,C-k) over bar obtained from neighbor- hood designs of Paley-type bipartite graphs P(q, k) and their complements, respectively for q an odd prime. We prove that for some values of q and k the codes C-q,C-k are self-dual and the codes (C-q,C-k) over bar are self-orthogonal. Most of these codes tend to be with optimal or near optimal parameters. Next, we extend the codes C(q,k )to get doubly even self dual codes and find that most of these codes ar...
On the Krall-type polynomials on q-quadratic lattices Alvarez-Nodarse, R.; Adiguzel, R. Sevinik (Elsevier BV, 2011-08-01) In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, q-basic series representation and three-term recurrence relations are obtained. In particular, the q-Racah-Krall polynomials obtained via the addition of two mass points to the weight function of the non-standard q-Racah polynomials at the ends of the interval of orthogonality are considered in detail. Some important limit cases are also discussed. (C) 2011 Royal Net...
On bounded and unbounded operators Uyanık, Elif; Yurdakul, Murat Hayrettin; Department of Mathematics (2017) In this thesis we study on bounded and unbounded operators and obtain some results by considering $ell$-K"{o}the spaces. As a beginning, we introduce some necessary and sufficient conditions for a Cauchy Product map on a smooth sequence space to be continuous and linear and we consider its transpose. We use the modified version of Zahariuta's method to obtain analogous results for isomorphic classification of Cartesian products of K"{o}the spaces. We also investigate the SCBS property and show that all sepa...
On affine variety codes from the Klein quartic Geil, Olav; Özbudak, Ferruh (Springer Science and Business Media LLC, 2019-03-01) We study a family of primary affine variety codes defined from the Klein quartic. The duals of these codes have previously been treated in Kolluru et al., (Appl. Algebra Engrg. Comm. Comput. 10(6):433-464, 2000, Ex. 3.2). Among the codes that we construct almost all have parameters as good as the best known codes according to Grassl (2007) and in the remaining few cases the parameters are almost as good. To establish the code parameters we apply the footprint bound (Geil and HOholdt, IEEE Trans. Inform. The...

Citation Formats

E. Martinez Moro, H. Özadam, F. Özbudak, and s. szabo, “On a class of repeated root monomial like abelian codes,” Journal of Algebra Combinatorics Discrete Structures and Applications, pp. 75–84, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42513.