A Characterization of Classes of Linear Ternary Codes over the GaloisField GF(3)

Mary Immaculate Okombo; Michael Onyango  Ojiema; Benard Kivunge; Vincent Marani

doi:10.51867/Asarev.Maths.2.1.3

Authors

Mary Immaculate Okombo Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya Author
Michael Onyango Ojiema Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya Author https://orcid.org/0000-0001-9635-7597
Benard Kivunge Department of Mathematics, Kenyatta University P.O. Box 43844-00100, Nairobi, Kenya Author https://orcid.org/0000-0002-4905-7783
Vincent Marani Department of Mathematics, Kibabii University, P. O. Box 1699 -50200, Bungoma, Kenya Author https://orcid.org/0000-0002-2170-7131

DOI:

https://doi.org/10.51867/Asarev.Maths.2.1.3

Abstract

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.

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