In this paper we prove that the class of Goppa codes whose polynomial is form $$g(x) = \textbf{Tr}_{{\mathbb {F}}_{q^{m}} \setminus {\mathbb {F}}_{q}}$$ where $$\textbf{Tr}_{{\mathbb a trace from field extension degree $$m \ge 3$$ has better minimum distance than what bound $$d 2\deg (g(x))+1$$ implies. This result significant improvement compared to Trace over quadratic extensions (the case 2$...

We study codes constructed from graphs where the code symbols are associated with the edges and the symbols connected to a given vertex are restricted to be codewords in a component code. In particular we treat such codes from bipartite expander graphs coming from Euclidean planes and other geometries. We give results on the minimum distances of the codes.

The optimal distance measure for a given discrimination task under the nearest neighbor framework has been shown to be the likelihood that a pair of measurements have different class labels [5]. For implementation and efficiency considerations, the optimal distance measure was approximated by combining more elementary distance measures defined on simple feature spaces. In this paper, we address...

This paper investigates the energy UMD of polygonal unknots. It provides equations for finding the energy for any planar regular n-gon and for any m-gon, where the vertices lie on the vertices of a regular m 2 -gon and on the midpoints of each edge. In addition, we show that a regular 4-gon minimizes the energy for any quadrilateral. Finally, this paper includes a proof showing that if we have ...

Minimum distance computations on complex geometry commonly employ hierarchies of bounding volumes that are pruned through establishment of upper and lower bounds. In this paper we describe a novel time coherence scheme which utilizes coherence on these bounds, rather than coherence derived from the geometry of the bounding volumes or from the geometry of the underlying model. This method is thu...

Total and average distance are not only interesting invariants of graphs in their own right but are also used for studying properties or classifying graphical systems that depend on the number of edges traversed. Recent examples include studies of computer networks [3] and the use of graphical invariants to partially classify the structure of molecules [1]. There have been a number of conjectur...

Suppose that N inputs to a linear, time-invariant channel are designed to maximize the minimum L , distance between channel outputs. It is assumed that all inputs are zero outside the finite time window [ T , TI and are constrained in energy. The jointly optimal inputs and channel frequency response H(f) for which the minimum distance is maximized is studied, subject to the constraint that the ...