Abstract:
This paper uses the modular
representation method to classify the internal
structures of degree 120 related to a group of
extension,𝑶𝟖
+ 𝟐 : 2.Specifically, we determine the
number of binary linear codes and construct their
lattice structure, as well as investigate the properties
of some linear codes and designs of minimum
weights. Our findings reveal that there are 12
binary linear codes, consisting of 4 doubly even
codes, 4 projective codes, 2 irreducible codes, and 2
decomposable codes. We also identify 2 primitive 1-
designs of minimum weight. The results
demonstrate the potential benefits of using linear
codes and designs from finite groups of extension
with modular representation methods, such as
improved error correction, increased data storage
capacity, improved security, efficient designs, and
improved computational efficiency. However, it is
important to note that this topic can be complex and
technical, and we recommend that stakeholders
collaborate with experts in the field to ensure the
accuracy and reliability of the information being
used. Overall, this study contributes to the
understanding of the modular representation
method and its applications in coding theory and
related field.
