English

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 GL2(C){\rm GL}_2(\mathbb{C}) 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