Abstract
This paper investigates the construction and analysis of binary linear codes and designs from the orthogonal group O?8(2). We employ the Key-Moori method and the modular theoretic approach to construct codes and designs from the primitive permutation representations of O?8(2) of degrees 119, 136, and 765. The study reveals the existence of optimal and near-optimal codes, as well as codes with desirable properties such as self-orthogonality and doubly-evenness. Connections between the codes and designs are explored, revealing interesting combinatorial structures. The findings contribute to the field of coding theory by providing new examples of codes with good parameters and to the understanding of the orthogonal group O?8(2) by revealing its rich submodule structure. The study also demonstrates the effectiveness of computational methods, such as MAGMA, in constructing and analyzing codes and designs from simple groups. Limitations and future research directions are discussed.
Keywords
Binary linear codes, combinatorial designs, orthogonal groups, O?8(2)
Citations
IRE Journals:
Elizabeth Masiga , Lucy Chikamai , Vincent Marani
"Binary Linear Codes and Designs from the Orthogonal Group O-8(2)" Iconic Research And Engineering Journals Volume 8 Issue 1 2024 Page 268-272
IEEE:
Elizabeth Masiga , Lucy Chikamai , Vincent Marani
"Binary Linear Codes and Designs from the Orthogonal Group O-8(2)" Iconic Research And Engineering Journals, 8(1)
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