Algebraic Decoding for Quadratic Residue Codes by Using Newton Identities

使用牛顿恒等式对二次余数码进行代数解码

• 批准号: 9016340
• 负责人: Irving Reed
• 金额: $ 33.02万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-04-15 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9016340&HistoricalAwards=false
• 关键词: Algebraic; Decoding; Quadratic; Residue; Codes

The primary objectives of this research are to find decoding algorithms for the Quadratic Residue (QR) Codes, including the well known (23,12,7) Golay code, the (31,16,7) QR code and the (41,21,9) code. The key idea is to find the error locator polynomial by a systematic use of the Newton identities associated with the code syndromes. The study focusses on the binary QR codes which have length 8m+/- 1. The techniques developed extend the algebraic decoding algorithm found recently by the PI for the (31,16,7) QR code and by Elia for the (23,12,7) Golay code to more general QR codes. The first new example of this extension is the (41,21,9) QR code. Is expected that this work and the algebraic methods developed here can apply generally to the entire set of QR codes and to other codes such as the BCH and Reed-Solomon codes.

这项研究的主要目标是找到用于二次残基（QR）代码的解码算法，包括众所周知的（23,12,7）Golay代码，（31,16,16,7）QR代码和（41,21,9）代码。 关键思想是通过系统地使用与代码综合症相关的牛顿身份来找到错误定位器多项式。 该研究的重点是具有长度为8M +/- 1的二进制QR码。开发的技术扩展了PI最近发现的代数解码算法（31,16,7）QR码，Elia和Elia for Elia for（23,12,7）Golay GoLay代码（23,12,7）GOLAY代码到达更多一般的QR代码。 该扩展程序的第一个新示例是（41,21,9）QR代码。 预计此处开发的这项工作和代数方法通常适用于整个QR码以及其他代码，例如BCH和REED - 固体代码。