Browsing by Author "Marani, Vincent Nyongesa"

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A Characterization of Classes of Linear Ternary Codes over the Galois Field GF(3)
(African Scientific Annual Review, 2025-07-07) Okombo, Mary Immaculate; Ojiema, Michael Onyango; Kivunge, Benard; Marani, Vincent Nyongesa
Linear cyclic ternary codes defined over the Galois field GF(3) exhibit several advantages over their binary counterparts. For instance, they provide an extra option for each pulse resulting into a larger set of available codes at any given length. This paper presents a comprehensive study of classes of linear cyclic ternary codes of length 25 ≤ n ≤ 50. While binary codes have been extensively studied, the properties and applications of longer ternary codes remain less explored. This study address this gap by providing an in-depth characterization of these codes for the stated lengths. Using computational methods implemented in Magma software, a diverse set of linear cyclic ternary codes over GF(3) were generated and analyzed. The paper provides a multifaceted characterization framework that integrates algebraic, combinatorial, and geometric perspectives, offering a holistic understanding of these codes. This study contributes to the theoretical advancement of non-binary codes and their practical applications in error correction, cryptography, and communication systems.
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
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
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.
Binding Number Bounds of Zero Divisor Graphs of Classes of Completely Primary Finite Rings
(African Scientific Annual Review, 2024-07-07) Mmasi, Eliud; Ojiema, Michael Onyango; Marani, Vincent Nyongesa
The binding number of a graph is an important graph parameter which measures the distribution of the size of the graph and its related properties including toughness, rapture degree, scattering number and its integrity. For complete graphs G ≃ Kn obtained from commutative finite ring, some results exist on the bounds of binding numbers. In this paper, we consider an incomplete but connected zero divisor graph Γ(R) associated with a class of completely primary finite ring R and use standard procedures to compute the binding number bounds, the average binding number and related graph parameters.
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.
Designs and Lattices from Classes of Cyclic Linear Ternary Codes over GF(3)
(Science Mundi, 2025-07-07) Okombo, Mary Immaculate; Ojiema, Michael Onyango; Kivunge, Benard; Marani, Vincent Nyongesa
In this study, we investigate the relationships between code parameters and lattice properties, providing new insights into the structure of ternary codes from a geometric perspective. Our findings extend the existing knowledge of ternary cyclic codes, particularly for lengths exceeding 25. We construct several new codes with favorable parameters, constructed previously unreported combinatorial designs, and characterized lattices with unique properties. The results demonstrate that ternary cyclic codes exhibit high structural regularity and often produce interesting designs and lattices with properties distinct from their binary counterparts. The research reveal strong interconnections between Coding Theory, Combinatorial Design Theory, and Lattice Theory in the context of ternary codes. We provide a multifaceted characterization framework that integrates algebraic, combinatorial, and geometric perspectives, offering a holistic understanding of these codes. This study contributes to the theoretical advancement of non-binary codes and opens new avenues for their practical applications in error correction, cryptography, and communication systems.
Graph Numbers and Distance Related Parameters of Zero Divisor Graphs
(Science Mundi, 2024-08-06) Mmasi, Eliud; Ojiema, Michael Onyango; Marani, Vincent Nyongesa
Distance-related parameters have applications in the field of pharmaceutical chemistry, network discovery, robot navigation, and optimizations. Cyclic structures exhibit significant topological features that have become important research areas in the field of computer science and mathematics. Due to the inherent algebraic relationship between graph numbers and distance related parameters, this paper characterizes variants of distance related parameters and graph numbers associated with the zero divisor graphs akin to cyclic structures obtained from classes of completely primary finite rings. In particular, we investigate the local fractional metric dimension and provide certain results concerning graph indices namely the Weiner index and the Zagreb index.
Mathematical Modelling and Optimal Controls for Controlling Pneumonia-HIV Co-Infection
(International Journal of Innovative Research & Development, 2021-01-07) Wafula, Nebert Kituni; Kwach, Boniface Otieno; Marani, Vincent Nyongesa
Bacterial infections like Pneumonia have emerged as an important cause of morbidity and mortality in individuals infected with HIV giving rise to their co-infection. There are mathematical models that describe; the co-dynamics, treatment and protection mechanisms of Pneumonia and HIV infections. Therefore, this research is aimed at determining optimal control treatments through developing a deterministic mathematical model Pneumonia-HIV coinfection incorporating the use of anti-pneumonia and ART treatment interventions as controls. The uncontrolled pneumonia-HIV co-infection is presented with its analysis. Finally, the optimal control theory for Pneumonia-HIV coinfection model is derived analytically by applying the Pontryagin’s Maximum Principle.
On Skew Quasi-P-Class (Q) Operators
(International Journal of Mathematics And its Applications, 2023-07-07) Wanjala Victor; Matuya, John Wanyonyi; Njuguna, Edward; Marani, Vincent Nyongesa
Skew quasi-p-class (Q) operator is introduced. We show that this class satisfies Bishop’s property. We equally show that this class is isoloid and polaroid. Results linking this class to other classes such as class (Q) are also given and a result showing that this class doesn’t preserve similarity of operators is outlined.