Classification of Some Internal Structures of Degree 120 Related To a Group of Extension𝑂8+ 2 : 2

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 fields.