| 摘要: |
| 里德-所罗门编码是最广泛使用的纠错码之一.介绍一种使用除法算法的解码方法,发展该算法的理论并讨论支持该算法的例子.最后,证明与该解码算法有关的一个概率上的定理,关于何时该方法是最有效的,得出一些概率上的结果. |
| 关键词: 里德-所罗门编码 除法算法 纠错码 |
| DOI： |
| 分类号: |
| 基金项目: |
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| Using the division algorithm to decode Reed-Solomon Codes |
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CHRISTINA banks-Turner1, MATTHEW Lennon2, EDUARDO Reynoso3, BRANDY Thibodeaux4, AMANDA Urquiza5, ASHLEY Wheatley6, DEREK Young7
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1.Department of Mathematics, Loyola Marymount University;2.Department of Mathematics, The Christ College;3.Department of Mathematics, California State University;4.Department of Mathematics, University of Louisiana at Lafayette;5.Department of Mathematics, Arizona State University;6.Department of Mathematical Sciences, Tennessee State University;7.Department of Mathematics, Iowa State University
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| Abstract: |
| Reed-Solomon codes are some of the most widely used error correcting codes. In this paper we introduce a decoding algorithmwhich utilizes the division algorithm. We develop theory and provide examples to support the algorithm. Lastly, we prove a theorem on probability related to this decoding algorithm and examine some probabilistic results on when this method is most effective. |
| Key words: Reed-Solomon division algorithm error-correcting codes |
