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On the Stabilizer of Weight Enumerators of Linear Codes
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.Comment: 11 pages. An improved and extended version of this paper has been
resubmitted at arXiv:1707.0057