We use the study of bilinear forms over a finite field to give a decomposition of the linear codes similar to the one in [10] for generalized toric codes. Such decomposition, called geometric decomposition of a linear code and which can be obtained in a constructive way, allows to express easily the dual of a linear code and gives a method to estimate the minimum distance. The proofs for charac...

The hull H(C) of a linear code C is defined by H(C) = C ∩ C⊥. A linear code with a complementary dual (LCD) is a linear code with H(C) = {0}. The dimension of the hull of a code is an invariant under permutation equivalence. For binary and ternary codes the dimension of the hull is also invariant under monomial equivalence and we show that this invariant is determined by the extended weight enu...

A three-dimensional Monte-Carlo (Potts) model was modified to incorporate the effect of grain-boundary inclination on boundary mobility. For this purpose, a straightforward geometric construction was developed to determine the local orientation of the grain-boundary plane. The combined effects of grain-boundary plane and misorientation on the effective grain-boundary mobility were incorporated ...

In a stereo image pair, the fundamental matrix encodes the rigidity constraint of the scene. It combines the internal parameters of both cameras (which can be the same) and their relative position and orientation. It associates to image points in one view the so-called epipolar line in the other view, which is the locus of projection of the same 3D point, whose particular position on the straig...

Abstract. A new morphological multiscale method in 3D image processing is presented which combines the image processing methodology based on nonlinear diffusion equations and the theory of geometric evolution problems. Its aim is to smooth level sets of a 3D image while simultaneously preserving geometric features such as edges and corners on the level sets. This is obtained by an anisotropic c...

Abstract. A new morphological multiscale method in 3D image processing is presented which combines the image processing methodology based on nonlinear diffusion equations and the theory of geometric evolution problems. Its aim is to smooth level sets of a 3D image while simultaneously preserving geometric features such as edges and corners on the level sets. This is obtained by an anisotropic c...

In recent years, projection device which has advanced its miniaturization and price reduction are attracted as display device against a backdrop of high needs for wide and high-definition screen. However, the expression of projector on non-special screen causes geometric problems of distorted expression caused by a surface shape of the screen and a positional relation among devices. To solve th...

The widespread utilization of QR code and its coincidence with the swift growth of e-commerce transactions have imposed the computer vision researchers to continuously devise a variety of QR code recognition algorithms. The latter performances are generally limited due to two main factors. Firstly, most of them are computationally expensive because of the implemented feature descriptor complexi...

A list decoding for an error-correcting code is a decoding algorithm that generates a list of codewords within a Hamming distance from the received vector, where can be greater than the error-correction bound. In [18], a list-decoding procedure for Reed–Solomon codes [19] was generalized to algebraic–geometric codes. A recent work [8] gives improved list decodings for Reed–Solomon codes and alg...