Construction of rational surfaces yielding good codes

Construction of rational surfaces yielding good codes

In the present article, we consider Algebraic Geometry codes on some rational surfaces. The estimate of the minimum distance is translated into a point counting problem on plane curves. This problem is solved by applying the upper bound à la Weil of Aubry and Perret together with the bound of Homma and Kim for plane curves. The parameters of several codes from rational surfaces are computed. Am...

Construction of Rational Surfaces of Degree 12 in Projective Fourspace

The aim of this paper is to present two different constructions of smooth rational surfaces in projective fourspace with degree 12 and sectional genus 13. In particular, we establish the existences of five different families of smooth rational surfaces in projective fourspace with the prescribed invariants.

Construction of Rational Elliptic Surfaces with Mordell-Weil Rank 4

A search for good convolutional codes to be used in the construction of turbo codes

Recursive systematic convolutional encoders have been shown to play a crucial role in the design of turbo codes. We recall some properties of binary convolutional encoders and apply them to a search for good constituent convolutional codes of turbo codes. Tables of the “best” recursive systematic convolutional encoders found are presented for various rates, together with the average bit-error p...

Rational Generalized Offsets of Rational Surfaces

The rational surfaces and their offsets are commonly used in modeling and manufacturing. The purpose of this paper is to present relationships between rational surfaces and orientation-preserving similarities of the Euclidean 3-space. A notion of a similarity surface offset is introduced and applied to different constructions of rational generalized offsets of a rational surface. It is shown th...