A5070013407- Coding theory and cryptography
- Finite Group Theory Research
- graph theory and CDMA systems
- Cancer Mechanisms and Therapy
- Islamic Finance and Communication
- Cooperative Communication and Network Coding
- Rings, Modules, and Algebras
- Algebraic structures and combinatorial models
- Error Correcting Code Techniques
- Mathematics and Applications
- Peptidase Inhibition and Analysis
- Cryptographic Implementations and Security
- Educational Methods and Media Use
- Advanced Mathematical Modeling in Engineering
- Differential Equations and Numerical Methods
- Differential Equations and Boundary Problems
- Commutative Algebra and Its Applications
- Point processes and geometric inequalities
- Quantum-Dot Cellular Automata
- Mechanisms of cancer metastasis
Sampoerna University
2017-2021
Northern Arizona University
2020
University of Chester
2020
Yıldız Technical University
2017
Bursa Orhangazi University
2015-2017
Fatih University
2012-2015
Ege University
1985
<p style='text-indent:20px;'>In this work, we describe a construction for self-dual codes in which employ group rings and reverse circulant matrices. By applying the directly over different alphabets, by employing well known extension neighbor methods were able to obtain extremal binary of lengths some have parameters that not literature before. In particular, constructed three new length 64, twenty-two 68, twelve 80 four 92.
We describe a composite construction from group rings where the groups have orders 16 and 8. This is then applied to find extremal binary self-dual codes with parameters [32, 16, 8] or 6]. also extend this by expanding search field which enables us more above different of automorphism groups. These are lifted
In this correspondence, we consider quadratic double and bordered circulant construction methods over the ring R := F2 + uF2 u 2 F2, where 3 = 1.Among other examples, extremal binary self-dual codes of length 66 are obtained by these constructions.These extended using extension theorems for as a result 8 new 68 obtained.More precisely, with β=117, 120, 133 in W68,1 γ 1, β=49, 57, 59 γ=2, β=69, 81 W68,2 constructed first time literature.The generators available online at [7].In addition to...
We study cyclic codes over commutative local Frobenius rings of order 16 and give their binary images under a Gray map which is generalization the maps on 4. prove that are quasi-cyclic index 4 examples various lengths constructed from these techniques including new optimal codes.
In this work, we study construction methods for self-dual and formally codes from group rings, arising the cyclic group, dihedral dicyclic semi-dihedral group. Using these constructions over rings $ \mathbb{F}_2+u \mathbb{F}_2 \mathbb{F}_4+u \mathbb{F}_4 $, obtain 9 new extremal binary of length 68 25 even with parameters [72,36,14] $.
Abstract In this work, we define composite matrices which are derived from group rings. We extend the idea of G -codes to -codes. show that these codes ideals in a ring, where ring is finite commutative Frobenius and an arbitrary group. prove dual -code also -code. quasi-composite Additionally, study generator matrices, consist identity matrices. Together with well known extension method, neighbour method its generalization, find extremal binary self-dual length 68 new weight enumerators for...
Abstract In this work, we describe a double bordered construction of self-dual codes from group rings. We show that is effective for groups order 2 p where odd, over the rings $\mathbb {F}_{2}+u\mathbb {F}_{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>F</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>+</mml:mo> <mml:mi>u</mml:mi> </mml:math> and {F}_{4}+u\mathbb {F}_{4}$ <mml:mn>4</mml:mn> . demonstrate importance new by finding many...
We describe a bordered construction for self-dual codes coming from group rings. apply the constructions cyclic and dihedral groups over several alphabets to obtain extremal binary of various lengths. In particular we find new code length 78.
In this work, four circulant and quadratic double (QDC) constructions are applied to the family of rings R_k,m. Self-dual binary codes obtained as Gray images self-dual QDC over Extremal length 64 ?-four R_2,1 R_2,2. lengths 66 68 constructed by applying extension theorems F_2 these codes. More precisely, 11 new 39 discovered. The with weight enumerators for first time in literature. results tabulated.