Given an abstract group G, an N dimensional orthogonal matrix representation G of G, and an “initial vector” x ∈ R , Slepian defined the group code generated by the representation G to be the set of vectors Gx. If G is a group of permutation matrices, the set Gx is called a “permutation code”. For permutation codes a ’stack algorithm’ decoder exists that, in the presence of low noise, produces ...

A novel construction of Mixed Parity Code for secret message communication is presented in this paper. Mixed Parity Code is a tool for secured data transmission with bit error control mechanism. The construction procedure of this code is provided based on the choices of existing error control codes and existing message character sets. Crypto-code words are prepared by the combinations of messag...

The presence of pronounced inequalities in mortality and life expectancy across income, education and social groups has long been a “stylized fact” of demography. Research across a large number of developed and wealthy countries, including Ireland, has shown that those with fewer resources, less education or a lower occupational class have higher standardised mortality rates (SMRs) than more ad...

In order to study circuit complexity classes within NC in a uniform setting we need a uniformity condition which is more restrictive than those in common use Two such conditions stricter than NC uniformity Ru Co have appeared in recent research Immerman s families of circuits de ned by rst order formulas Im a Im b and a unifor mity corresponding to Buss deterministic log time reductions Bu We s...

We show that ACC0 is precisely what can be computed with constant-width circuits of polynomial size and polylogarithmic genus. This extends a characterization given by Hansen, showing that planar constant-width circuits also characterize ACC0. Thus polylogarithmic genus provides no additional computational power in this model. We consider other generalizations of planarity, including crossing n...

STEP (STandard for the Exchange of Product model data, ISO 10303) data for numerical control, or STEP-NC, is intended to provide full product and process data interoperability between computer-aided manufacturing systems and machine tool controllers. Numerous prototype and several commercial implementations of STEP-NC are currently being developed. Testing is an essential step toward ensuring c...

We give a recursion-theoretic characterization of the complexity classes NC for k ≥ 1. In the spirit of implicit computational complexity, it uses no explicit bounds in the recursion and also no separation of variables is needed. It is based on three recursion schemes, one corresponds to time (time iteration), one to space allocation (explicit structural recursion) and one to internal computati...

We derive an effective Lagrangian for meson fields. This is done in the light-cone gauge for two-dimensional large-Nc QCD by using the bilocal auxiliary field method. The auxiliary fields are bilocal on light-cone space and their Fourier transformation determines the parton momentum distribution. As the first test of our method, the ’t Hooft equation is derived from the effective Lagrangian. E-...