论文标题
在矩阵上可能对树代码有用
On matrices potentially useful for tree codes
论文作者
论文摘要
在[1]中研究的一个概念中，我们考虑了矩阵的属性，而不是有限领域的属性，该特性将三角形完全非矩阵概括以阻止矩阵。我们表明，（1）具有此属性的矩阵足以构造良好的树代码，（2）在二次大小的字段上一个随机的块三角矩阵可以满足此属性。我们还将表明，这种随机结构的概括会产生代码，而不是二次尺寸字段，其速率和最小相对距离的总和将任意接近1。
Motivated by a concept studied in [1], we consider a property of matrices over finite fields that generalizes triangular totally nonsingular matrices to block matrices. We show that (1) matrices with this property suffice to construct good tree codes and (2) a random block-triangular matrix over a field of quadratic size satisfies this property. We will also show that a generalization of this randomized construction yields codes over quadratic size fields for which the sum of the rate and minimum relative distance gets arbitrarily close to 1.
