Advances in Mathematics of Communications
August 2019 , Volume 13 , Issue 3
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In this paper, some general properties of the Zeng-Cai-Tang-Yang cyclotomy are studied. As its applications, two constructions of frequency-hopping sequences (FHSs) and two constructions of FHS sets are presented, where the length of sequences can be any odd integer larger than 3. The FHSs and FHS sets generated by our construction are (near-) optimal with respect to the Lempel–Greenberger bound and Peng–Fan bound, respectively. By choosing appropriate indexes and index sets, a lot of (near-) optimal FHSs and FHS sets can be obtained by our construction. Furthermore, some of them have new parameters which are not covered in the literature.
We investigate subspace codes whose codewords are subspaces of
In communication networks theory the concepts of networkness and network surplus have recently been defined. Together with transmission and betweenness centrality, they were based on the assumption of equal communication between vertices. Generalised versions of these four descriptors were presented, taking into account that communication between vertices
At Eurocrypt 2015, Barbulescu et al. introduced two new methods of polynomial selection, namely the Conjugation and the Generalised Joux-Lercier methods, for the number field sieve (NFS) algorithm as applied to the discrete logarithm problem over finite fields. A sequence of subsequent works have developed and applied these methods to the multiple and the (extended) tower number field sieve algorithms. This line of work has led to new asymptotic complexities for various cases of the discrete logarithm problem over finite fields. The current work presents a unified polynomial selection method which we call Algorithm
We show that there is a binary subspace code of constant dimension 3 in ambient dimension 7, having minimum subspace distance 4 and cardinality 333, i.e.,
This is achieved by a more general technique for an exhaustive search in a finite group that does not depend on the enumeration of all subgroups.
There are two standard approaches to the construction of
In this paper, by analyzing the quadratic factors of an
We show that under certain conditions every maximal symmetric subfield of a central division algebra with positive unitary involution
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