On the Stabilizer of Weight Enumerators of Linear Codes
Martino Borello, Olivier Mila
TL;DR
This paper explores the relationship between linear codes and their weight enumerator stabilizers, providing a classification of codes with infinite stabilizers, an algorithm for computation, and applications to Reed-Muller codes.
Contribution
It offers a complete classification of linear codes with infinite stabilizers and an efficient algorithm to compute stabilizers of weight enumerators.
Findings
Finiteness of stabilizers proved for certain codes
Complete classification of codes with infinite stabilizer
Reed-Muller codes can have trivial stabilizers
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.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Error Correcting Code Techniques