On the Stabilizer of Weight Enumerators of Linear Codes
Abstract
This paper investigates the relation between linear codes and the stabilizer in GL2(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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