Due to the editorial process, there may be slight discrepancies between this version and the published one. Abstract|The problem of minimizing the vertex count at a given time index in the trellis for a general (nonlinear) code is shown to be NP-complete. Examples are provided that show that 1) the minimal trellis for a nonlinear code may not be observable, i.e., some codewords may be represent...

Two global gyrokinetic codes are benchmarked against each other by comparing simulation results in the case of ion temperature gradient driven (ITG) turbulence, in the adiabatic electron response limit. The two codes are the Eulerian code GENE and the Lagrangian Particle-In-Cell code ORB5 which solve the gyrokinetic equations. Linear results are presented, including growth rates, real frequenci...

We present a code for the simulation of laser–plasma interaction processes relevant for applications in inertial confinement fusion. The code consists of a fully nonlinear hydrodynamics in two spatial dimensions using a Lagrangian, discontinuous Galerkin-type approach, a paraxial treatment of the laser field and a spectral treatment of the dominant non-local transport terms. The code is fully p...

For rate R = 1=2 convolutional codes with 16 states there exists a gap between Heller’s upper bound on the free distance and its optimal value. This correspondence reports on the construction of 16state, binary, rate R = 2=4 nonlinear trellis and convolutional codes having dfree = 8; a free distance that meets the Heller upper bound. The nonlinear trellis code is constructed from a 16-state, ra...

SnadiOpt is a package that supports the use of the automatic differentiation package ADIFOR with the optimization package Snopt. Snopt is a general-purpose system for solving optimization problems with many variables and constraints. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for large-scale linear an...

In recent years, much work has been done on implementing a variety of algorithms in nonlinear programming software. In this paper, we analyze the performance of several stateof-the-art optimization codes on large-scale nonlinear optimization problems. Extensive numerical results are presented on different classes of problems, and features of each code that make it efficient or inefficient for e...

The Nordstrom-Robinson code NR is a non-linear binary code of length 16, with 2 codewords and minimum distance 6. Its automorphism group is a semidirect product of an elementary abelian group of order 16 and the alternating group A7. This group and the corresponding action of A7 is also at the origin of the sporadic A7-geometry. We construct this geometry and derive the Nordstrom-Robinson code ...

We present upper bounds on the size of codes that are locally testable by querying only two input symbols. For linear codes, we show that any 2-locally testable code with minimal distance δn over any finite field F cannot have more than |F| codewords. This result holds even for testers with two-sided error. For general (non-linear) codes we obtain the exact same bounds on the code size as a fun...

Improved bounds for A(n,d), the maximum number of codewords in a (linear or nonlinear) binary code of word length n and minimum distance d, and for A (n&u), the maximum number of binary vectors of length n, distance d, and constant weight w in the range n 5 24 and d 5 10 are presented. Some of the new values are A (9,4) = 20 (which was previously believed to follow from the results of Wax), A (...