• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Designs, Codes and Cryptography >Generalized MacWilliams identities and their applications to perfect binary codes
【24h】

Generalized MacWilliams identities and their applications to perfect binary codes

机译：广义MacWilliams身份及其在完善二进制代码中的应用

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

We present generalized MacWilliams identities for binary codes. These identities naturally lead to the concepts of the local weight distribution of a binary code with respect to a word u and its MacWilliams u-transform. In the case that u is the all-one word, these ones correspond to the weight distribution of a binary code and its MacWilliams transform, respectively. We identify a word v with its support, and consider v as a subset of {1, 2,..., n}. For two words u,w of length n such that their intersection is the empty set, define the u-face centered at w to be the set {z Èw : z Í u}{{z cup w : z subseteq u}} . A connection between our MacWilliams u-transform and the weight distribution of a binary code in the u-face centered at the zero word is presented. As their applications, we also investigate the properties of a perfect binary code. For a perfect binary code C, the main results are as follows: first, it is proved that our local weight distribution of C is uniquely determined by the number of codewords of C in the orthogonal u-face centered at the zero word. Next, we give a direct proof for the known result, concerning the weight distribution of a coset of C in the u-face centered at the zero word, by A. Y. Vasil’eva without using induction. Finally, it is proved that the weight distribution of C in the orthogonal u-face centered at w is uniquely determined by the codewords of C in the u-face centered at the zero word.
机译：我们提供二进制代码的广义MacWilliams身份。这些身份自然导致了相对于单词u及其MacWilliams u变换的二进制代码的局部权重分布的概念。在u是全字的情况下，这些分别对应于二进制代码的权重分布及其MacWilliams变换。我们确定单词v及其支持，并将v视为{1，2，...，n}的子集。对于长度为n的两个单词u，w以使它们的交点为空集合，将以w为中心的u面定义为集合{zÈw：zÍu} {{z cup w：zsubseteq u}}。给出了MacWilliams u变换和以0字为中心的u面中二进制代码的权重分布之间的联系。作为它们的应用程序，我们还研究了完美的二进制代码的属性。对于一个完美的二进制码C，主要结果如下：首先，证明了我们的C的局部权重分布是唯一地由以零字为中心的正交u面中C的代码字的数目确定的。接下来，我们直接给出已知结果的证明，涉及A. Y. Vasil’eva在不使用归纳法的情况下，以0字为中心的u面中C的陪集的权重分布。最后，证明了以w为中心的正交u面中C的权重分布由以0字为中心的u面中C的码字唯一地确定。

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