Results 1 to 10 of about 12,109 (35)
An efficient high dimensional quantum Schur transform [PDF]
Quantum, 2018 The Schur transform is a unitary operator that block diagonalizes the action of the symmetric and unitary groups on an n fold tensor product V⊗n of a vector space V of dimension d.
H. Krovi
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On the Efficiency of Polar-Like Decoding for Symmetric Codes [PDF]
IEEE Transactions on Communications, 2021 The recently introduced polar codes constitute a breakthrough in coding theory due to their capacity-achieving property. This goes hand in hand with a quasilinear construction, encoding, and successive cancellation list decoding procedures based on the ...
K. Ivanov, R. Urbanke
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Duality of averaging of quantum states over arbitrary symmetry groups revealing Schur–Weyl duality [PDF]
Journal of Physics A: Mathematical and Theoretical, 2022 It is a well-established fact in quantum information theory, that uniform averaging over the collective action of a unitary group on a multipartite quantum state projects the state to a form equivalent to a permutation operator of the subsystems.
M. Markiewicz, Janusz Przewocki
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New Lower Bounds for Permutation Codes Using Linear Block Codes [PDF]
IEEE Transactions on Information Theory, 2019 In this paper we prove new lower bounds for the maximal size of permutation codes by connecting the theory of permutation codes with the theory of linear block codes. More specifically, using the columns of a parity check matrix of an $[{\it{ n,k,d}}]_{
Giacomo Micheli, Alessandro Neri
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New Differentially 4-Uniform Piecewise Permutations over F22k from the Inverse Function
Symmetry, 2023 Permutations with low differential uniformity, high nonlinearity and high algebraic degree over F22k are preferred substitution boxes in modern block ciphers.
Shuai Li, Li Miao
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Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes [PDF]
IEEE Transactions on Information Theory, 2007 We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the tradeoff between performance and complexity of iterative decoding for the binary erasure channel.
T. Hehn +3 more
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On the existence of block-transitive combinatorial designs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2010 Block-transitive Steiner t-designs form a central part of the study of highly symmetric combinatorial configurations at the interface of several disciplines, including group theory, geometry, combinatorics, coding and information theory, and cryptography.
Michael Huber
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Infinite families of 3‐designs from APN functions [PDF]
Journal of combinatorial designs (Print), 2019 Combinatorial t ‐designs have nice applications in coding theory, finite geometries, and several engineering areas. A classical method for constructing t ‐designs is by the action of a permutation group that is t ‐transitive or t ‐homogeneous on a point ...
Chunming Tang
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Isomorphisms of subcategories of fusion systems of blocks and Clifford theory
, 2020 Let k be an algebraically closed field of prime characteristic p. Let G be a finite group, let N be a normal subgroup of G, and let c be a G-stable block of kN so that (kN)c{(kN)c} is a p-permutation G-algebra. As in Section 8.6 of [M. Linckelmann, The
M. E. Harris
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The Rubiks Cubes in Group Theory
Theoretical and Natural Science, 2023 This paper expounds the basic concept of group theory and its application in Rubiks Cube transformation and restoration formula. The different states of the magic cube are regarded as the elements of the magic cube group, and the set generated by six ...
Jialun Yu, Wenxin Li
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