權重為3 的最優避免衝突碼

Abstract

如果一個集合C包含於(Z_2)^n的全部向量都是漢明權重為 k，且在C 裡任意兩個向量的循環移動距離至少為2k-2， 則我們稱此集合C 是一個長度為n 且權重為k 的衝突避免 碼。在本論文中，我們用某些類型的數列，得到了建構長 度為n = 4m (m 為奇數)且權重為3 的最優避免衝突碼的 方法。再加上一些已知結果，我們完全解決了如何建構長 度為偶數且權重為3 的最優避免衝突碼的問題。

A conflict-avoiding code of length n and weight k is defined as a set C Contains in (Z_2)^n of binary vectors, called codewords, all of Hamming weight k such that the distance of arbitrary cyclic shifts of two distinct codewords in C is at least 2k-2. In this thesis, we obtain direct constructions for optimal conflict-avoiding codes of length n = 4m where m is odd and weight 3 by using certain types of sequences which are newly constructed. As a consequence (with known results), we have completely settled the problem of constructing optimal con°ict-avoiding codes of even length and weight 3.