藉由二元向量到排列的對映之排列碼建構法

Abstract

本論文中, 我們持續探討如何建構從二元向量到排列的對映. 我們成功地建構出改善目前最好的排列碼邊界的對映. 由於建構這些對映的流程大致相同, 我們提出一個如何建構這特定系列對映的大綱. 另外注意到我們的對映可能不是保持長度相等, 我們將說明非保持長度對映存在的必要性. 如果只使用保持長度的對映, 會失去很多可以改進的空間.

In this paper, we continue the study of constructing distance-increasing mappings from binary vectors to permutations. We successfully construct some mappings which induce better lower bounds for permutation codes than the current existing one : P(n,r)>=A(n,r-1). Since the approaches for constructing our mappings are similar, we give a framework for constructing a certain class of mappings. Note that our mappings may not be length-preserving. We will show the necessity of non-length-preserving mappings. We will lose many improvements if we only use length-preserving mappings.