Kibuspace
Kibuspace is the institutional repository of Kibabii University, the repository preserves the University's research legacy and all aspects of knowledge generated by KIBU community for posterity
Communities in DSpace
Select a community to browse its collections.
Recent Submissions
A Self Dual and Doubly Even Code Related to Mathieu Group M24
(IRE Journals, 2021-03-07) Marani, Vincent Nyongesa
In this paper, we determine a self-dual and doubly even [24,12,8] code. We determine and discuss the properties of designs related to this code 2010 Mathematics Subject Classification: 94B 05C
Analysis of Generalised Boussinesq Coupled Equations Using Lie Symmetry
(IRE Journals, 2022-03-07) Omari, Sarah; Marani, Vincent Nyongesa; Oduor, Michael
In the last decades, Nonlinear partial differential equations (NPDEs) have become essential tools to model complex phenomena that arise in different aspects of science and engineering such as hydrodynamics. Therefore, constructing exact and approximate solutions of NLPDEs is of great importance in mathematical sciences. Previously authors have done similar work with restriction of K and L to be one. In this paper we solve the generalised Boussinesq coupled equations:
𝒖𝒕 + 𝑲𝒗𝒙 + 𝑳𝒖𝒖𝒙 = 𝟎; 𝑲 > 𝟎; 𝑳 > 𝟎 𝒗𝒕 + 𝒖𝒗𝒙 + 𝒖𝒙𝒙𝒙 = 𝟎
using Lie symmetry of differential equations where u = u (x; t) is the velocity of water and v = v (x; t) the total depth of water and subscripts denote partial derivatives. The positive constants K, L would enable further analysis of optimal water depth and velocity
be determined.
An Irreducible and Doubly Even Code of Degree 23 Related to Mathieu Group M23
(IRE Journals, 2021-04-07) Marani, Vincent Nyongesa
In this paper, we determine an irreducible and doubly even code [23,11,8]. We determine and discuss the properties of designs related to this code
Classification of Some Internal Structures of Degree 120 Related To a Group of Extension𝑂8+ 2 : 2
(IRE Journals, 2023-08-07) Maina, Janet Lilian; Matuya, John Wanyonyi; Njuguna, Edward; Marani, Vincent Nyongesa
This paper uses the modular representation method to classify the internal structures of degree 120 related to a group of extension,𝑶𝟖+ 𝟐 : 2.Specifically, we determine the number of binary linear codes and construct their lattice structure, as well as investigate the properties of some linear codes and designs of minimum weights. Our findings reveal that there are 12 binary linear codes, consisting of 4 doubly even codes, 4 projective codes, 2 irreducible codes, and 2 decomposable codes. We also identify 2 primitive 1-designs of minimum weight. The results demonstrate the potential benefits of using linear codes and designs from finite groups of extension with modular representation methods, such as improved error correction, increased data storage capacity, improved security, efficient designs, and improved computational efficiency. However, it is important to note that this topic can be complex and technical, and we recommend that stakeholders collaborate with experts in the field to ensure the accuracy and reliability of the information being used. Overall, this study contributes to the understanding of the modular representation method and its applications in coding theory and related fields.
Conjugacy Classes of the Split Extension 28: U4(2)
(IRE Journals, 2024-08-07) Wekesa, Caroly Wafula; Chikamai, Lucy Walingo; Marani, Vincent Nyongesa
This study presents a comprehensive analysis of the conjugacy classes of the split extension 28: U4(2), where U4(2) is the unitary group of degree 4 over the field with 2 elements. Using a combination of theoretical techniques, including Fischer-Clifford matrices and character theory, along with computational tools such as GAP and MAGMA, we determined and classified all 49 conjugacy classes of this group. Our analysis revealed complex fusion patterns from U4(2) to 28: U4(2), including class splitting and the introduction of new element orders. We found that 28: U4(2) has more than double the number of conjugacy classes compared to U4(2) alone, with class sizes ranging from 5 to over 1.3 million elements. This work addresses significant gaps in the existing literature regarding this specific group extension and provides insights into its structure, representations, and automorphisms. The methodology and results presented here contribute to the broader understanding of group extensions and lay the groundwork for further investigations into the properties and applications of 28: U4(2) in areas such as coding theory and quantum mechanics.