随机SAF路由的格上编码
Codes on Lattices for Random SAF Routing
摘要：
本文利用格中元素的唯一分解构造了一类等重码。讨论了格的唯一准素分解和唯一不可约分解的条件，建立了格与Noether交换环的理想分解之间的联系。在这种情况下，它表明，借鉴的权威作品Dilworth，沃德和其他人，即，相对于诺特交换环，存在唯一的不可约分解格不保证唯一的主要分解。在我们提出的建设的源字母表是一组唯一可分解的元素构造从一个选定的子集的不可约或适当的格的主要元素。两个晶格元素之间的距离函数基于构成元素集合之间的对称距离。已知构造这样的等重码等价于构造具有适当参数的Johnson图。一些界限上的代码的大小也提出了一种方法来获得最佳大小的代码，利用约翰逊图描述的代码，进行了讨论。作为一个应用程序，我们展示了如何这些代码可以用于错误和擦除纠正随机网络采用存储和转发（SAF）路由。
英文摘要：
In this paper, a construction of constant weight codes based on the unique decomposition of elements in lattices is presented. The conditions for unique primary decomposition and unique irreducible decomposition in lattices are discussed and connections with the decomposition of ideals in Noetherian commutative rings established. In this context it is shown, drawing on the definitive works of Dilworth, Ward and others, that, as opposed to Noetherian commutative rings, the existence of unique irreducible decomposition in lattices does not guarantee unique primary decomposition. The source alphabet in our proposed construction is a set of uniquely decomposable elements constructed from a chosen subset of irreducible or primary elements of the appropriate lattice. The distance function between two lattice elements is based on the symmetric distance between sets of constituent elements. It is known that constructing such constant weight codes is equivalent to constructing a Johnson graph with appropriate parameters. Some bounds on the code sizes are also presented and a method to obtain codes of optimal size, utilizing the Johnson graph description of the codes, is discussed. As an application we show how these codes can be used for error and erasure correction in random networks employing store-and-forward (SAF) routing.
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