Any linear code with a nontrivial automorphism has the structure of a module over a polynomial ring. The theory of Griihner bases for modules gives a compact description and implementation of a systematic encoder. We present examples of algebraic-geometric Goppa codes that can be encoded by these methods, including the one-point Hermitian codes. Index TermsSystematic encoding, algebraic-geometr...

This paper will detail the capabilities of a new geometric modeling tool, called Geodesic, which is being released in source code form to the general community. In addition to providing geometric operations to create geometry useful in MEMS simulation, it uniquely offers a fully integrated 3-D levelset kernel that permits highly accurate physically based deposition and etching simulation.

In this paper we study the algebraic geometry of any two-point code on the Hermitian curve and reveal the purely geometric nature of their dual minimum distance. We describe the minimum-weight codewords of many of their dual codes through an explicit geometric characterization of their supports. In particular, we show that they appear as sets of collinear points in many cases.

For a linear [n, k, d] code, it is well known that d ≤ n−k+1 (see [12]), and when d = n−k+1, it is called the MDS code (maximum distance separable). For every n ≤ q + 1 there is an MDS [n, k, d] code for any given k and d satisfying d = n − k + 1. It is just the geometric codes on a rational curve (see [15]). There is a long-standing conjecture about the MDS linear codes that is called the main...

In this work, the natural geometric relation between the space time block code design for the unknown channel at the receiver and its counterpart design for the known channel at the receiver is exploited, to establish an estimate on the corresponding diversities. This leads to a decomposition result and splits the code design problem into two complexity reduced sub tasks. Moreover a geometrical...

In this paper we introduce the idea of using Computer Vision techniques for improving and enhancing watermarking capabilities. Specifically, we incorporate Geometric Hashing techniques into the watermarking methodology. Geometric Hashing was developed to detect objects in a visual scene under a class of geometric transformations. The technique is incorporated into watermarking to detect waterma...

We study the generalized and extended weight enumerator of the qary Simplex code and the q-ary first order Reed-Muller code. For our calculations we use that these codes correspond to a projective system containing all the points in a finite projective or affine space. As a result from the geometric method we use for the weight enumeration, we also completely determine the set of supports of su...

For a linear code C of length n and dimension k, Wolf noticed that the trellis state complexity s(C) of C is upper bounded by w(C) := min(k, n− k). In this paper we point out some new lower bounds for s(C). In particular, if C is an Algebraic Geometric code, then s(C) ≥ w(C) − (g − a), where g is the genus of the underlying curve and a is the abundance of the code.

We present a general purpose code analyzer and generator for filtered predicates, which are critical for geometric algorithms. While there already exist such code generators, our contribution is to generate ”almost static filters”, a type of filter which could not be generated previously. The generated and safe filtered predicates are almost as fast as their inexact floating point counterparts,...

Problem statement: Cryptosystem using linear codes was developed in 1978 by Mc-Eliece. Later in 1985 Niederreiter and others developed a modified version of cryptosystem using concepts of linear codes. But these systems were not used frequently because of its larger key size. In this study we were designing a cryptosystem using the concepts of algebraic geometric codes with smaller key size. Er...