• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Designs, Codes and Crytography >Division of trinomials by pentanomials and orthogonal arrays
【24h】

Division of trinomials by pentanomials and orthogonal arrays

机译：通过五项式和正交数组对三项式进行除法

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Consider a maximum-length binary shift-register sequence generated by a primitive polynomial f of degree m. Let C_n~f denote the set of all subintervals of this sequence with length n, where m ＜ n ≤ 2m, together with the zero vector of length n. Munemasa (Finite fields Appl, 4(3): 252-260,1998) considered the case in which the polynomial f generating the sequence is a trinomial satisfying certain conditions. He proved that, in this case, C_n~f corresponds to an orthogonal array of strength 2 that has a property very close to being an orthogonal array of strength 3. Munemasa's result was based on his proof that very few trinomials of degree at most 2m are divisible by the given trinomial f. In this paper, we consider the case in which the sequence is generated by a pentanomial f satisfying certain conditions. Our main result is that no trinomial of degree at most 2m is divisible by the given pentanomial f, provided that f is not in a finite list of exceptions we give. As a corollary, we get that, in this case, C_n~f corresponds to an orthogonal array of strength 3. This effectively minimizes the skew of the Hamming weight distribution of subsequences in the shift-register sequence.
机译：考虑由度为m的原始多项式f生成的最大长度二进制移位寄存器序列。令C_n〜f表示该序列的所有子间隔的集合，其长度为n，其中m ＜n≤2m，以及长度为零的零向量。 Munemasa（Finite field Appl，4（3）：252-260,1998）考虑了生成序列的多项式f是满足某些条件的三项式的情况。他证明了，在这种情况下，C_n〜f对应于强度2的正交数组，该属性具有非常接近强度3的正交数组的特性。Munemasa的结果是基于他的证明：极小二项式最多2m可被给定的三项式f整除。在本文中，我们考虑由满足一定条件的五项式f生成序列的情况。我们的主要结果是，给定的五项式f不能将至多2m的三项式除以整除，只要f不在我们给出的有限例外中。作为推论，在这种情况下，我们得出C_n〜f对应于强度3的正交数组。这有效地最小化了移位寄存器序列中子序列的汉明权重分布的偏斜。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号