List decoding of q-ary Reed-Muller codes
文献类型：期刊论文
| 作者 | Pellikaan, R; Wu, XW |
| 刊名 | IEEE TRANSACTIONS ON INFORMATION THEORY
 |
| 出版日期 | 2004-04-01 |
| 卷号 | 50期号:4页码:679-682 |
| 关键词 | Guruswami-Sudan algorithm list decoding order domain q-ary Reed-Muller (RM) codes subfield subcodes |
| ISSN号 | 0018-9448 |
| DOI | 10.1109/TIT.2004.825043 |
| 英文摘要 | The q-ary Reed-Muller (RM) codes RMq(u,m) of length n = q(m) are a generalization of Reed-Solomon (RS) codes, which use polynomials in m variables to encode messages through functional encoding. Using an idea of reducing the multivariate case to the univariate case, randomized list-decoding algorithms for RM codes were given in [1] and [15]. The algorithm in [15] is an improvement of the algorithm in [1], it is applicable to codes RMq(u,m) with u < q/2 and works for up to E < n (1-root2u/q) errors. In this correspondence, following [6], we show that q-ary RM codes are subfield subcodes; of RS codes over F-qm. Then, using the list-decoding algorithm in [5] for RS codes over F,m, we present a list-decoding algorithm for q-ary RM codes. This algorithm is applicable to codes of any rates, and achieves an error-correction bound n(1-root(n-d)/n). The algorithm achieves a better error-correction bound than the algorithm in [15], since when u is small n (1-root/(n-d)/n) = n(1-1rootu/q) The implementation of the algorithm requires O (n) field operations in F-q and O(n(3)) field operations in F-qm under some assumption. |
| WOS研究方向 | Computer Science ; Engineering |
| 语种 | 英语 |
| WOS记录号 | WOS:000220475700010 |
| 出版者 | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/482]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Pellikaan, R |
| 作者单位 | 1.Tech Univ Eindhoven, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Pellikaan, R,Wu, XW. List decoding of q-ary Reed-Muller codes[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2004,50(4):679-682. |
| APA | Pellikaan, R,&Wu, XW.(2004).List decoding of q-ary Reed-Muller codes.IEEE TRANSACTIONS ON INFORMATION THEORY,50(4),679-682. |
| MLA | Pellikaan, R,et al."List decoding of q-ary Reed-Muller codes".IEEE TRANSACTIONS ON INFORMATION THEORY 50.4(2004):679-682. |
入库方式： OAI收割
来源：数学与系统科学研究院
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