Error correcting codes from general linear groups
Mahir Bilen Can · Journal of Algebra and Its Applications · 2025
This paper introduces families of algebro-geometric codes associated with the general linear groups and special linear groups. We explore their parameters and investigate the geometry of the underlying varieties by determining the hyperplane sections with the minimum and maximum number of rational points. For the specific case of [Formula: see text], we explicitly determine the full MacWilliams weight enumerator polynomial. Furthermore, we show that the [Formula: see text]-code has a Griesmer defect of precisely 1.