We will show how to make a linear code from a configuration of affine lines in general position and a suitable set of rational points on it. The number of rational points on our singular curve is beyond the Weil bound and their coordinates are quite easy to compute. We will show a new decoding procedure which originates from the configuration. It is expected our method may correct errors less t...

The successful application to elliptic curve cryptography of side-channel attacks, in which information about the secret key can be recovered from the observation of side channels like power consumption, timing, or electromagnetic emissions, has motivated the recent development of unified formulæ for elliptic curve point operations. In this paper, we show how an attack introduced by Walter can ...

This paper describes a novel image transform called Multi-Scale Autoconvolution which is invariant with respect to affine transformations of the spatial image coordinates. The transform can be applied directly to image patches without segmentation. Algebraically, the transform is simple requiring only rescaling of the image and computation of two-dimensional convolutions that can be performed e...

In this paper, we propose an adaptation of the Itoh-Tsujii algorithm to the frequency domain for efficient inversion in a class of Optimal Extension Fields. To the best of our knowledge, this is the first time a frequency domain finite field inversion algorithm is proposed for elliptic curve cryptography. We believe the proposed algorithm would be well suited especially for efficient low-power ...

Hardware and algorithmic optimization techniques are presented to the left-shift, right-shift, and the traditional Euclideanmodular inverse algorithms. Theoretical arguments and extensive simulations determined the resulting expected running time. On many computational platforms these turn out to be the fastest known algorithms for moderate operand lengths. They are based on variants of Euclide...

It is widely known that, for the affine camera model, both shape and motion data can be factorised directly from the measurement matrix containing the image coordinates of the tracked feature points. However, classical algorithms for Structure from Motion (SfM) are not robust: measurement outliers, that is, incorrectly detected or matched feature points can destroy the result. A few methods to ...

Much local government has been utilizing a large-scale digital map using Geographic Information System (GIS). However, the maintenance and renewal of a map database need much labor and time. Moreover, the updating method of a map has not been established yet and there have been almost no successful examples. The purpose of the study is to establish a method of updating the large-scale map for l...

For a fixed positive integer k, consider the collection of all affine hyperplanes in n-space given by xi − x j = m, where i, j ∈ [n], i 6= j , and m ∈ {0, 1, . . . , k}. Let Ln,k be the set of all nonempty affine subspaces (including the empty space) which can be obtained by intersecting some subset of these affine hyperplanes. Now give Ln,k a lattice structure by ordering its elements by rever...

A subcube partition is a of the Boolean cube $\{0,1\}^n$ into subcubes. irreducible if only sub-partitions whose union are singletons and entire partition. tight it “mentions” all coordinates.
 We study extremal properties partitions: minimal size, weight, maximal number points, minimum dimension. also consider existence homogeneous partitions, in which subcubes have same dimensions. addit...

We show that $T \bar T, J T$ and $J T_a$ - deformed classical CFTs possess an infinite set of symmetries take the form a field-dependent generalization two-dimensional conformal transformations. If, in addition, seed affine $U(1)$ symmetry, we it also survives theories, again form. These can be understood as infinitely-extended underlying CFT, seen through prism "dynamical coordinates" characte...