Browsing by Author "Ojiema, Michael Onyango"

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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.
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.
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.