## Tsukuba Journal of Mathematics

### Ring of the weight enumerators of $d_n^+$

#### Abstract

We show that the ring of the weight enumerators of a self-dual doubly even code $d_n^+$ in arbitrary genus is finitely generated. Indeed enough elements to generate it are given. The latter result is applied to obtain a minimal set of generators of the ring in genus two.

#### Article information

Source
Tsukuba J. Math., Volume 42, Number 1 (2018), 53-63.

Dates
Revised: 8 March 2018
First available in Project Euclid: 7 November 2018

https://projecteuclid.org/euclid.tkbjm/1541559648

Digital Object Identifier
doi:10.21099/tkbjm/1541559648

Mathematical Reviews number (MathSciNet)
MR3873531

Zentralblatt MATH identifier
07055224

Keywords
code weight enumerator

#### Citation

Fujii, Makoto; Oura, Manabu. Ring of the weight enumerators of $d_n^+$. Tsukuba J. Math. 42 (2018), no. 1, 53--63. doi:10.21099/tkbjm/1541559648. https://projecteuclid.org/euclid.tkbjm/1541559648