2003/11/04 by Gabriele Nebe, Eric M. Rains, Nebe, Gabriele +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #13A50 #94B05 #94B60 #Cellular Automata and Applications #DNA and Biological Computing #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.math/0311046
openalex publication_date 2003/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main theorem in this paper is a far-reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary-genus weight enumerators of self-dual codes defined over a large class of finite rings and modules. The proof of the theorem uses a categorical approach, and will be the subject of a forthcoming book. However, the theorem can be stated and applied without using category theory, and we illustrate it here by applying it to generalized doubly-even codes over fields of characteristic 2, doubly-even codes over the integers modulo a power of 2, and self-dual codes over the noncommutative ring \Fq + \Fq u, where u2 = 0..