Binary Linear Codes and Designs from the Orthogonal Group O-8(2)

References

[1] MacWilliams, F. J., & Sloane, N. J. A. (1977). The theory of error-correcting codes. North-Holland Publishing Company.

[2] Huffman, W. C., & Pless, V. (2003). Fundamentals of error-correcting codes. Cambridge University Press.

[3] Pless, V. (1998). Introduction to the theory of error-correcting codes (3rd ed.). John Wiley & Sons.

[4] Wilson, R. A. (2009). The finite simple groups. Springer Science & Business Media.

[5] Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A., & Wilson, R. A. (1985). Atlas of finite groups: Maximal subgroups and ordinary characters for simple groups. Oxford University Press.

[6] Ding, C., & Li, C. (2020). Codes from Designs and Graphs. World Scientific.

[7] Assmus, E. F., & Key, J. D. (1992). Designs and their codes. Cambridge University Press.

[8] Chikamai, K. L. (2021). Codes and designs from simple groups: A survey. Journal of Algebra and Its Applications, 20(2), 2130001.

[9] Maina, P. M., Mbaale, F., & Musyoka, P. (2023). Codes and designs from the orthogonal group. Journal of Algebra Combinatorics Discrete Structures and Applications, 10(1), 1-15.

[10] Bosma, W., Cannon, J., & Playoust, C. (1997). The Magma algebra system I: The user language. Journal of Symbolic Computation, 24(3-4), 235-265.

[11] Moori, J., & Rodrigues, B. G. (2020). A comparative analysis of codes from symmetric designs and graph-theoretic codes. Electronic Notes in Discrete Mathematics, 70, 35-40.

[12] G¨uzeltepe, M., & Heden, O. (2021). On codes generated by the incidence matrices of some designs. Advances in Mathematics of Communications, 15(1), 113-130.

[13] Key, J. D., & Moori, J. (1995). Designs, codes and graphs from the Janko groups J1 and J2. Journal of Combinatorial Mathematics and Combinatorial Computing, 40, 143-159.

[14] Cheng, D., & Sloane, N. J. A. (1992). The automorphism group of a certain extremal code. Proceedings of the American Mathematical Society, 116(3), 875-879.

[15] Tonchev, V. D. (1998). Codes and designs. In Handbook of Coding Theory (pp. 1229-1268). Elsevier Science.

[16] Malik, M., & Malik, A. (2022). Applications of coding theory in cryptography: A survey. In Advances in Information Communication Technology and Computing (pp. 13-22). Springer, Singapore.

[17] Rani, S., & Gupta, S. (2021). A survey on applications of coding theory in various fields. In Advances in Communication and Computational Technology (pp. 1079-1088). Springer, Singapore.

[18] Joyner, D., Kreminski, R., & Turisco, J. (2021). Applied Abstract Algebra with MapleTM and MATLAB® (3rd ed.). CRC Press.

[19] Brouwer, A. E., Cohen, A. M.,& Neumaier, A. (1989). Distance-regular graphs. Springer-Verlag.

[20] Godsil, C., & Royle, G. (2001). Algebraic graph theory. Springer-Verlag.

[21] Wilson, R. A. (2009). The finite simple groups. Springer Science & Business Media.

[22] Key, J. D., & Moori, J. (1999). Codes, designs and graphs from the Janko group J1. Journal of Combinatorial

@article{1706061,
      author = {Elizabeth Masiga, Lucy Chikamai, Vincent Marani},
      title = {Binary Linear Codes and Designs from the Orthogonal Group O-8(2)},
      journal = {Iconic Research And Engineering Journals},
      year = {2024},
      volume = {8},
      number = {1},
      pages = {268-272},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1706061.pdf},
      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)},
      month = {July},
  }