Coding theory and the Mathieu groups
نویسندگان
چکیده
منابع مشابه
The Mathieu groups and designs
In the early 80-ties it became clear that the classification of the non-abelian finite simple groups was complete. Among the finite simple groups we find several families: the alternating groups and various families of groups of Lietype and their twisted analogues. Besides these families there exist 26 sporadic finite simple groups. In these notes we consider five sporadic simple groups, the Ma...
متن کاملMathieu Groups
In this essay, we will discuss some interesting properties of the Mathieu groups, which are a family of five sporadic finite simple groups, as well as some closely related topics. One construction of the Mathieu groups involves Steiner systems, so we will begin by discussing Steiner systems.
متن کاملClifford quantum computer and the Mathieu groups
One learned from Gottesman-Knill theorem that the Clifford model of quantum computing [11] may be generated from a few quantum gates, the Hadamard, π/4-Phase and Controlled-Z gates, and efficiently simulated on a classical computer. We employ the group theoretical package GAP[10] for simulating the two qubit Clifford group C2. We already found that the symmetric group S(6), aka the automorphism...
متن کاملThe Mathieu groups and their geometries
In the early 80-ties it became clear that the classification of the non-abelian finite simple groups was complete. Among the finite simple groups we find several families: the alternating groups and various families of groups of Lietype and their twisted analogues. Besides these families there exist 26 sporadic finite simple groups. Buildings are natural geometries for the groups of Lie-type (a...
متن کاملThe Symmetric Genus of the Mathieu Groups
The (symmetric) genus of a finite group may be defined as the smallest genus of those closed orientable surfaces on which G acts faithfully as a group of automorphisms. In this paper the genus of each of the five Mathieu groups Mn, M12, M22, M23 and M24 is determined, with the help of some computer calculations and a little-known theorem of Ree on permutations.
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ژورنال
عنوان ژورنال: Information and Control
سال: 1971
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(71)90295-6