| Z16环上的二次剩余码 |
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| 引用本文： | 谭晓青.Z16环上的二次剩余码[J].数学研究与评论,2005,25(4). |
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| 作者姓名： | 谭晓青 |
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| 作者单位： | 暨南大学数学系,广东,广州,510632 |
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| 摘 要： | 本文研究了整数环模16剩余类环Z16上的二次剩余码,讨论了它们的幂等生成元及其扩展码的自对偶性等代数性质,并研究了码长为7的Z16二次剩余码在两种已有的Gray映射下的有趣性质,尤其是确定了它们的Lee重量分布.
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| 关 键 词： | 二次剩余码 幂等生成元 Gray映射 Hamming重量 Lee重量 |
Quadratic Residue Code over Z16 |
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| TAN Xiao-qing.Quadratic Residue Code over Z16[J].Journal of Mathematical Research and Exposition,2005,25(4). |
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| Authors: | TAN Xiao-qing |
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| Abstract: | In this paper, we study quadratic residue (QR) codes over integral ring mod 16 residue class ring Z16, and discuss their algebra properties, including their generator and the self-duality of their extended codes, etc. We also investigate some interesting properties of Z16-QR codes of length 7 under two kinds of Gray maps, and especially study their Lee weight distribution. |
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| Keywords: | quadratic residue code idempotent generator Gray map Hamming weight Lee weight |
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