A Family Of Low Density Matrices In Lagrangian–Grassmannian

Abstract

The aim of this paper is twofold. First, we show a connection between the Lagrangian- Grassmannian variety geometry defined over a finite field with q elements and the q-ary Low-Density Parity- Check codes. Second, considering the Lagrangian-Grassmannian variety as a linear section of the Grassmannian variety, we prove that there is a unique linear homogeneous polynomials family, up to linear combination, such that annuls the set of its rational points.

Keywords

• lagrangian-grassmannian variety
• general theory of matrices
• the low-density parity-check codes
• 14m15
• 15b34
• 94b05