Return an iterator going through all elements in self. The fastest iteration is the parabolic iteration and the depth first algorithm without tracking words is second. Return the positive roots of self.
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Return the right coset representatives of self for the parabolic subgroup generated by the simple reflections in J. Return the reflection along the given root.
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Finite complex reflection groups. Group algebras of root lattice realizations. The point of entry to work with reflection groups is ReflectionGroup which can be used with finite Cartan-Killing types: sage: ReflectionGroup [ 'A' , 2 ] optional - gap3 Irreducible real reflection group of rank 2 and type A2 sage: ReflectionGroup [ 'F' , 4 ] optional - gap3 Irreducible real reflection group of rank 4 and type F4 sage: ReflectionGroup [ 'H' , 3 ] optional - gap3 Irreducible real reflection group of rank 3 and type H3.
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Irreducible p-constant characters of finite reflection groups : Journal of Group Theory
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Regular elements of finite reflection groups
Browse All Figures Return to Figure. Previous Figure Next Figure. The new optimal group codes from exceptional reflection groups that are obtained achieve high rates and have excellent distance properties. The decoding regions for maximum-likelihood ML decoding are explicitly characterized and an efficient ML-decoding algorithm is presented.
This algorithm relies on an extension of Slepian's decoding of permutation modulation and has similar low complexity,. Article :. Date of Publication: Mar DOI:
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