Codes and Invariant Theory
Abstract
The main theorem in this paper is a farreaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrarygenus weight enumerators of selfdual 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 doublyeven codes over fields of characteristic 2, doublyeven codes over the integers modulo a power of 2, and selfdual codes over the noncommutative ring $\F_q + \F_q u$, where $u^2 = 0$..
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2003
 arXiv:
 arXiv:math/0311046
 Bibcode:
 2003math.....11046N
 Keywords:

 Mathematics  Number Theory;
 Computer Science  Information Theory;
 94B05;
 13A50;
 94B60