On the Stabilizer of Weight Enumerators of Linear Codes

Martino Borello; Olivier Mila

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arXiv · 1511.00803

On the Stabilizer of Weight Enumerators of Linear Codes

Martino Borello·Olivier Mila

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Abstract

This paper investigates the relation between linear codes and the stabilizer in ${\rm GL}_2(\mathbb{C})$ 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.

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Martino Borello, Olivier Mila. 2017-07-04. On the Stabilizer of Weight Enumerators of Linear Codes. https://arxiv.org/abs/1511.00803

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