New Lower Bounds for Permutation Codes using Linear Block Codes [PDF]
arXiv, 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 $[n,k,d]_q$ linear block code, we are able to prove the existence of a permutation code in the symmetric group of ...
Giacomo Micheli, Alessandro Neri
arxiv +3 more sources
An efficient high dimensional quantum Schur transform [PDF]
Quantum, 2019 The Schur transform is a unitary operator that block diagonalizes the action of the symmetric and unitary groups on an $n$ fold tensor product $V^{\otimes n}$ of a vector space $V$ of dimension $d$.
Hari Krovi
doaj +3 more sources
Block cipher construction using minimum spanning tree from graph theory and its application with image encryption. [PDF]
Sci ProgIn modern cryptography, Substitution Boxes (S-boxes) are critical in introducing confusion into ciphertext, significantly enhancing encryption security. With the rising sophistication of hacking techniques, there is a growing need to develop stronger and
Rasheed MW +3 more
europepmc +2 more sources
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 ...
Huber, Michael
core +6 more sources
Stability of the replica-symmetric saddle-point in general mean-field spin-glass models [PDF]
, 2010 Within the replica approach to mean-field spin-glasses the transition from ergodic high-temperature behaviour to the glassy low-temperature phase is marked by the instability of the replica-symmetric saddle-point.
Andreas Engel +20 more
core +2 more sources
Towards Understanding Inductive Bias in Transformers: A View From Infinity
International Conference on Machine LearningWe study inductive bias in Transformers in the infinitely over-parameterized Gaussian process limit and argue transformers tend to be biased towards more permutation symmetric functions in sequence space.
Gur-Ari, Guy, Lavie, Itay, Ringel, Zohar
core +2 more sources
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
semanticscholar +1 more source
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
semanticscholar +1 more source
Rank three innately transitive permutation groups and related $2$-transitive groups [PDF]
Innov. Incidence Geom. 20 (2023) 135-175, 2022 The sets of primitive, quasiprimitive, and innately transitive permutation groups may each be regarded as the building blocks of finite transitive permutation groups, and are analogues of composition factors for abstract finite groups. This paper extends classifications of finite primitive and quasiprimitive groups of rank at most $3$ to a ...
arxiv +1 more source
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
semanticscholar +1 more source