組合編碼的簡介

Abstract

中文摘要

我們研究比較有組合性質的碼，如 super imposed codes, Reed-Muller Codes, Punctured Reed-Muller Codes, Hexacode, Extended Golay Code 和 Convolutional Codes等。我們探討這些碼和投影空間(projective geometries), 仿射空間(affine geometries),甚至一般的 ranked poset 的關係。

Abstract

We study codes with more combinatorial properties involved than algebraic properties. These include super imposed codes, Reed-Muller Codes, Punctured Reed-Muller Codes, Hexacode, Extended Golay Code and Convolutional Codes, most of them are related to the incidence structure on the projective geometries, affine geometries, or some ranked posets.