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The purpose of this paper is to collect computations related to the weight enumerators and to present some relationships among invariant rings. The latter is done by combining two maps, the Brou´e–Enguehard map and Igusa’s ρ homomorphism. For the completeness of the story, some formulae are given which are not necessarily used in the present manuscript. Sections 1 and 2 contain no new result
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