MDS和Reed-Muller码的树宽
The Treewidth of MDS and Reed-Muller Codes
摘要：
线性码的图形实现的约束复杂度是实现中局部约束码的最大维数。线性码的树宽是其任何无环图形实现的最小约束复杂度。这个概念提供了一个有用的参数化的线性码的最大似然解码复杂度。在本文中，我们证明了一个令人惊讶的事实，即对于最大距离可分码和Reed-Muller码，树宽等于网格宽度，其中，对于一个码，被定义为是其任何网格实现的最小约束复杂度（或分支复杂度）。从这一点上，我们得到确切的表达式，这些代码的树宽，这构成了唯一已知的明确表达式的代数码的树宽。
英文摘要：
The constraint complexity of a graphical realization of a linear code is the maximum dimension of the local constraint codes in the realization. The treewidth of a linear code is the least constraint complexity of any of its cycle-free graphical realizations. This notion provides a useful parametrization of the maximum-likelihood decoding complexity for linear codes. In this paper, we prove the surprising fact that for maximum distance separable codes and Reed-Muller codes, treewidth equals trelliswidth, which, for a code, is defined to be the least constraint complexity (or branch complexity) of any of its trellis realizations. From this, we obtain exact expressions for the treewidth of these codes, which constitute the only known explicit expressions for the treewidth of algebraic codes.
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