منابع مشابه
Permutation codes invariant under isometries
The symmetric group Sn on n letters is a metric space with respect to the Hamming distance. The corresponding isometry group is well known to be isomorphic to the wreath product Sn oS2. A subset of Sn is called a permutation code or a permutation array, and the largest possible size of a permutation code with minimum Hamming distance d is denoted by M(n, d). Using exhaustive search by computer ...
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We investigate the von Neumann entanglement entropy as function of the size of a subsystem for permutation invariant ground states in models with finite number of states per site, e.g., in quantum spin models. We demonstrate that the entanglement entropy of n sites in a system of length L generically grows as log2 2 en L−n /L +C, where is the on-site spin and C is a function depending only on m...
متن کاملThe permutation group of affine-invariant extended cyclic codes
The extended cyclic codes of length p” , p a prime, which are invariant under the aff ine-group acting on ffpm, are called affine-invariant codes. Following recent results of Berger, we present the formal expression of the permutat ion group of these codes. Afterwards we give several tools in order to determine effectively the group of a given code or of some infinite class of codes. W e next p...
متن کاملPermutationally Invariant Codes for Quantum Error Correction
A permutationally invariant n-bit code for quantum error correction can be realized as a subspace stabilized by the non-Abelian group Sn. The code corresponds to bases for the trivial representation, and all other irreducible representations, both those of higher dimension and orthogonal bases for the trivial representation, are available for error correction. A number of new (non-additive) cod...
متن کاملPermutation codes
There are many analogies between subsets and permutations of a set, and in particular between sets of subsets and sets of permutations. The theories share many features, but there are also big differences. This paper is a survey of old and new results about sets (and groups) of permutations, concentrating on the analogies and on the relations to coding theory. Several open problems are describe...
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ژورنال
عنوان ژورنال: Physical Review A
سال: 2014
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.90.062317