SISO Decoding of Z4 Linear Kerdock and Preparata Codes

Some nonlinear codes, such as Kerdock and Preparata codes, can be represented as binary images under the Gray map of linear codes over rings. This paper introduces MAP decoding of Kerdock and Preparata codes by working with their quaternary representation (linear codes over Z4 ) with the complexity of O(N2log2N), where N is the code length in Z4. A sub-optimal bitwise APP decoder with good error-correcting performance and complexity of O(Nlog2N) that is constructed using the decoder lifting technique is also introduced. This APP decoder extends upon the original lifting decoder by working with likelihoods instead of hard decisions and is not limited to Kerdock and Preparata code families. Simulations show that our novel decoders significantly outperform several popular decoders in terms of error rate

Constructions of Generalized Concatenated Codes and Their Trellis-Based Decoding Complexity

In this correspondence, constructions of generalized concatenated (GC) codes with good rates and distances are presented. Some of the proposed GC codes have simpler trellis omplexity than Euclidean geometry (EG), Reed–Muller (RM), or Bose–Chaudhuri–Hocquenghem (BCH) codes of approximately the same rates and minimum distances, and in addition can be decoded with trellis-based multistage decoding up to their minimum distances. Several codes of the same length, dimension, and minimum distance as the best linear codes known are constructed

Self-Dual Codes

Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory. Topics covered in this survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems, bounds, mass formulae, enumeration, extremal codes, open problems. There is a comprehensive bibliography.Comment: 136 page

Numerical simulations of granular dynamics II: Particle dynamics in a shaken granular material

Surfaces of planets and small bodies of our Solar System are often covered by a layer of granular material that can range from a fine regolith to a gravel-like structure of varying depths. Therefore, the dynamics of granular materials are involved in many events occurring during planetary and small-body evolution thus contributing to their geological properties. We demonstrate that the new adaptation of the parallel N-body hard-sphere code pkdgrav has the capability to model accurately the key features of the collective motion of bidisperse granular materials in a dense regime as a result of shaking. As a stringent test of the numerical code we investigate the complex collective ordering and motion of granular material by direct comparison with laboratory experiments. We demonstrate that, as experimentally observed, the scale of the collective motion increases with increasing small-particle additive concentration. We then extend our investigations to assess how self-gravity and external gravity affect collective motion. In our reduced-gravity simulations both the gravitational conditions and the frequency of the vibrations roughly match the conditions on asteroids subjected to seismic shaking, though real regolith is likely to be much more heterogeneous and less ordered than in our idealised simulations. We also show that collective motion can occur in a granular material under a wide range of inter-particle gravity conditions and in the absence of an external gravitational field. These investigations demonstrate the great interest of being able to simulate conditions that are to relevant planetary science yet unreachable by Earth-based laboratory experiments

Old Dogs, New Tricks: Authoritarian Regime Persistence Through Learning

How does diffusion lead to authoritarian regime persistence? Political decisions, regardless of what the actors involved might believe or espouse, do not happen in isolation. Policy changes, institutional alterations, regime transitions-- these political phenomena are all in some part a product of diffusion processes as much as they are derived from internal determinants. As such, political regimes do not exist in a vacuum, nor do they ignore the outside world. When making decisions about policy and practice, we should expect competent political actors to take a look at the wider external world. This dissertation project presents a theory of regime learning and authoritarian persistence to augment the extant literature on diffusion and democratization. While this literature provides important links between the outcomes across borders, it also falls short in explaining if and how diffusion can explain the absence of change-- authoritarian persistence. The new theoretical approach is rooted in concepts drawn from the democratization literature as well as the psychology of learning, and distinguishes simplistic learning (emulation)-- based on the availability heuristic-- and a more sophisticated learning process rooted in the representativeness heuristic. To test the implications of this theory, I develop a pair of new measures of change: liberalization (making concessions) and deliberalization (increasing repression). Using a combination of human and machine coding of yearly Freedom House country reports, I determine whether authoritarian regimes made liberalizing or deliberalizing moves which fall short of the significant regime changes that aggregate measures such as POLITY, Freedom House, and similar capture. An empirical examination employing these new measures reveals that diffusion does exist among authoritarian regimes at the regional level, among contiguous neighborhoods, and within more carefully confined groups of peers. These results add to our understanding of persistent authoritarianism and establish that emulation can be identified. Although authoritarian regimes seem to be be copying the liberalization and deliberalization strategies of their peers, there is not clear support for more sophisticated learning processes at this time