For pt.I see ibid., vol.34, no.5, p.1123-51 (1988). The family of Barnes-Wall lattices (including D/sub 4/ and E/sub 8/) of lengths N=2/sup n/ and their principal sublattices, which are useful in constructing coset codes, are generated by iteration of a simple construction called the squaring construction. The closely related Reed-Muller codes are generated by the same construction. The principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions, which also exhibit the interrelationships between codes and lattices of different lengths. An extension called the cubing construction generates good codes and lattices of lengths N=3*2/sup n/, including the Golay code and Leech lattice, with the use of special bases for 8-space. Another related construction generates the Nordstrom-Robinson code and an analogous 16-dimensional nonlattice packing. These constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum-likelihood decoding algorithms.
展开▼
机译：关于第一部分，见同上，第34卷第5期，第1123-51页（1988年）。长度为N = 2 / sup n /的Barnes-Wall晶格族（包括D / sub 4 /和E / sub 8 /）及其主要子格，可用于构造陪集代码，是通过简单的迭代生成的施工称为平方施工。紧密相关的里德-穆勒码由相同的结构生成。这些代码和格的主要属性是迭代平方结构的一般属性的结果，这些性质也表现出不同长度的代码和格之间的相互关系。一个扩展称为cubing结构，使用8空间的特殊基数生成了良好的代码和长度N = 3 * 2 / sup n /的格，包括Golay代码和Leech格。另一个相关的构造生成Nordstrom-Robinson码和类似的16维非晶格堆积。这些结构由网格图表示，这些网格图显示了它们的结构和相互关系，并导致有效的最大似然解码算法。
展开▼
