Results 41 to 50 of about 2,328 (103)
Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers [PDF]
, 2012 We introduce a new class of pseudoprimes-so called "overpseudoprimes to base $b$", which is a subclass of strong pseudoprimes to base $b$. Denoting via $|b|_n$ the multiplicative order of $b$ modulo $n$, we show that a composite $n$ is overpseudoprime if
Castillo, John H. +3 more
core +1 more source
Binary Cyclic Codes from Explicit Polynomials over $\gf(2^m)$
, 2013 Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over finite fields
Ding, Cunsheng, Zhou, Zhengchun
core +2 more sources
On the minimal period of integer tilings
Bulletin of the London Mathematical Society, Volume 57, Issue 4, Page 1160-1170, April 2025.Abstract If a finite set A$A$ tiles the integers by translations, it also admits a tiling whose period M$M$ has the same prime factors as |A|$|A|$. We prove that the minimal period of such a tiling is bounded by exp(c(logD)2/loglogD)$\exp (c(\log D)^2/\log \log D)$, where D$D$ is the diameter of A$A$.
Izabella Łaba, Dmitrii Zakharov
wiley +1 more source
Application of Constacyclic codes to Quantum MDS Codes
, 2014 Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian construction ...
Chen, Bocong, Ling, San, Zhang, Guanghui
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On the parameterized Tate construction
Journal of Topology, Volume 18, Issue 1, March 2025.Abstract We introduce and study a genuine equivariant refinement of the Tate construction associated to an extension Ĝ$\widehat{G}$ of a finite group G$G$ by a compact Lie group K$K$, which we call the parameterized Tate construction (−)tGK$(-)^{t_G K}$.
J. D. Quigley, Jay Shah
wiley +1 more source
Totally deranged elements of almost simple groups and invariable generating sets
Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.Abstract By a classical theorem of Jordan, every faithful transitive action of a non‐trivial finite group has a derangement (an element with no fixed points). The existence of derangements with additional properties has attracted much attention, especially for faithful primitive actions of almost simple groups.
Scott Harper
wiley +1 more source
Recovering p$p$‐adic valuations from pro‐p$p$ Galois groups
Journal of the London Mathematical Society, Volume 109, Issue 5, May 2024.Abstract Let K$K$ be a field with GK(2)≃GQ2(2)$G_K(2) \simeq G_{\mathbb {Q}_2}(2)$, where GF(2)$G_F(2)$ denotes the maximal pro‐2 quotient of the absolute Galois group of a field F$F$. We prove that then K$K$ admits a (non‐trivial) valuation v$v$ which is 2‐henselian and has residue field F2$\mathbb {F}_2$. Furthermore, v(2)$v(2)$ is a minimal positive
Jochen Koenigsmann, Kristian Strommen
wiley +1 more source
New constructions for disjoint partial difference families and external partial difference families
Journal of Combinatorial Designs, Volume 32, Issue 4, Page 190-213, April 2024.Abstract Recently, new combinatorial structures called disjoint partial difference families (DPDFs) and external partial difference families (EPDFs) were introduced, which simultaneously generalize partial difference sets, disjoint difference families and external difference families, and have applications in information security.
Sophie Huczynska, Laura Johnson
wiley +1 more source
Octonionic Magical Supergravity, Niemeier Lattices, and Exceptional & Hilbert Modular Forms
Fortschritte der Physik, Volume 72, Issue 2, February 2024.Abstract The quantum degeneracies of Bogomolny‐Prasad‐Sommerfield (BPS) black holes of octonionic magical supergravity in five dimensions are studied. Quantum degeneracy is defined purely number theoretically as the number of distinct states in charge space with a given set of invariant labels.
Murat Günaydin, Abhiram Kidambi
wiley +1 more source
A Family of Binary Sequences with Optimal Correlation Property and Large Linear Span
, 2005 A family of binary sequences is presented and proved to have optimal correlation property and large linear span. It includes the small set of Kasami sequences, No sequence set and TN sequence set as special cases.
Hu, Lei, Liu, Qingchong, Zeng, Xiangyong
core +1 more source