On the Stabilizer of Weight Enumerators of Linear Codes
Information Theory
2017-07-05 v2 Combinatorics
math.IT
Abstract
This paper investigates the relation between linear codes and the stabilizer in of their weight enumerators. We prove a result on the finiteness of stabilizers and give a complete classification of linear codes with infinite stabilizer in the non-binary case. We present an efficient algorithm to compute explicitly the stabilizer of weight enumerators and we apply it to the family of Reed-Muller codes to show that some of their weight enumerators have trivial stabilizer.
Keywords
Cite
@article{arxiv.1511.00803,
title = {On the Stabilizer of Weight Enumerators of Linear Codes},
author = {Martino Borello and Olivier Mila},
journal= {arXiv preprint arXiv:1511.00803},
year = {2017}
}
Comments
11 pages. An improved and extended version of this paper has been resubmitted at arXiv:1707.00575