Models of encoding and decoding via Grobner basis for algebraic geometry codes and multidimensional cyclic codes

基于 Grobner 基的代数几何码和多维循环码的编码和解码模型

• 批准号: 19760269
• 负责人: MATSUI Hajime
• 金额: $ 1.18万
• 依托单位: Toyota Technological Institute
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19760269/
• 关键词: 誤り訂正符号; 離散フーリエ変換; リード・ソロモン符号; エルミート曲線符号; 代数幾何符号; 代数曲線符号; グレブナー基底; 有限体; バールカンプ・マッシイアルゴリズム; 誤り訂正符合; ユークリッド・アルゴリズム; 代数典線符号

Research results are classified into three subjects as follows. 1. Searching algebraic curves that have many rational points and searching efficient codes on algebraic curves and multidimensional cyclic codes. A method to compute Grobner basis for generalized quasi-cyclic codes has been established, and thereby, a searching method for them has been established. 2. Constructing unified models of encoding and decoding system for codes on algebraic curves. 3. Application of unified system of encoding and decoding for Reed-Solomon codes. The circuit scale of the unified system for the next-generation error-correcting codes has been estimated as 40% reduction of that of the conventional system.

研究结果分为以下三个主题。1.搜索具有多个有理点的代数曲线，搜索代数曲线上的有效码和多维循环码。建立了广义拟循环码的Grobner基的计算方法，从而建立了广义拟循环码的搜索方法。2.构造代数曲线上码的编译码系统的统一模型。3. Reed-Solomon码统一编译码系统的应用。下一代纠错码的统一系统的电路规模估计为传统系统的40%减少。

项目成果

Systematic encoding for finite geometry LDPC codes based on Grobner bases

基于 Grobner 基的有限几何 LDPC 码的系统编码

• 发表时间: 2007
• 作者: V. Van;H. Matsui;S. Mita
• 通讯作者: S. Mita

A Simple Proof of Horiguchi's Error-Value Formula in Decoding of Alternant Codes and Its Applications

• DOI: 10.1587/transfun.e92.a.2146
• 发表时间: 2009-08
• 期刊: IEICE Trans. Fundam. Electron. Commun. Comput. Sci.
• 作者: H. Matsui

Complexity reduction of encoding and decoding for algebraic-geometric codes by discrete Fourier transforms

通过离散傅立叶变换降低代数几何码编码和解码的复杂度

• 发表时间: 2008
• 期刊: 豊田研究報告 No.61
• 作者: K. Ichige;K. Saito;H. Arai;松井一
• 通讯作者: 松井一

An effective systematic encoder implementation for generalized quasi-cyclic codes based on Grobner bases

基于 Grobner 基的广义准循环码的有效系统编码器实现

• 发表时间: 2009
• 作者: V.T. Van;H. Matsui;S. Mita
• 通讯作者: S. Mita

Generalized quasi-cyclic low-density parity-check codes based on finite geometries

基于有限几何的广义准循环低密度奇偶校验码

• 发表时间: 2009
• 作者: Vo Tam Van;Hajime Matsui;Seiichi Mita
• 通讯作者: Seiichi Mita