Jamison sequences in countably infinite discrete Abelian groups

Weak discrete logarithms in non-abelian groups

The intractability of the traditional discrete logarithm problem (DLP) forms the basis for the design of numerous cryptographic primitives. In [2] M. Sramka et al. generalize the DLP to arbitrary finite groups. One of the reasons mentioned for this generalization is P. Shor’s quantum algorithm [4] which solves efficiently the traditional DLP. The DLP for a nonabelian group is based on a particu...

Unextendible Sequences in Finite Abelian Groups

Let G = Cn1 ⊕ . . . ⊕ Cnr be a finite abelian group with r = 1 or 1 < n1| . . . |nr, and let S = (a1, . . . , at) be a sequence of elements in G. We say S is an unextendible sequence if S is a zero-sum free sequence and for any element g ∈ G, the sequence Sg is not zero-sum free any longer. Let L(G) = dlog2 n1e + . . . + dlog2 nre and d∗(G) = ∑r i=1(ni−1), in this paper we prove, among other re...

Filter Banks on Discrete Abelian Groups

In this work we provide polyphase, modulation, and frame theoretical analyses of a filter bank on a discrete abelian group. Thus, multidimensional or cyclic filter banks as well as filter banks for signals in `(Z×Zs) or `(Zr ×Zs) spaces are studied in a unified way. We obtain perfect reconstruction conditions and the corresponding frame bounds.

Inverse optimization in countably infinite linear programs

Given the costs and a feasible solution for a linear program, inverse optimization involves finding new costs that are close to the original ones and make the given solution optimal. We develop an inverse optimization framework for countably infinite linear programs using the weighted absolute sum metric. We reformulate this as an infinite-dimensional mathematical program using duality. We prop...

Error Bounds in Countably Infinite Spaces