Sign in
Back
The joint weight enumerator of an LCD code and its dual
Journal article   Open access  Peer reviewed

The joint weight enumerator of an LCD code and its dual

Adel Alahmadi, Michel Deza, Mathieu Dutour-Sikirić and Patrick Solé
Discrete Applied Mathematics, Vol.257, pp.12-18
31/03/2019
DOI: https://doi.org/10.1016/j.dam.2018.10.032

Abstract

LCD code Linear binary code Linear programming bounds
A binary linear code is called LCD if it intersects its dual trivially. We show that the coefficients of the joint weight enumerator of such a code with its dual satisfy linear constraints, leading to a new linear programming bound on the size of an LCD code of given length and minimum distance. In addition, we show that this polynomial is, in general, an invariant of a matrix group of dimension 4 and order 12. Also, we sketch a Gleason formula for this weight enumerator.
url
https://doi.org/10.1016/j.dam.2018.10.032View
Published (Version of record) Open

Metrics

1 Record Views

Details