Browsing by Author "Kivunge, Benard"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    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.
  • No Thumbnail Available
    Item
    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.