منابع مشابه
The Witt designs, Golay codes and Mathieu groups
Let V be a vector space over Fq with fixed basis e1, ..., en. A code C is a subset of V . A linear code is a subspace of V . The vector with all coordinates equal to zero (resp. one) will be denoted by 0 (resp. 1). The Hamming distance dH(u, v) between two vectors u, v ∈ V is the number of coordinates where they differ: when u = ∑ uiei, v = ∑ viei then dH(u, v) = |{i | ui 6= vi}|. The weight of...
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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...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1976
ISSN: 0021-8693
DOI: 10.1016/0021-8693(76)90107-1