环F_2+uF_2+…+u^(k-1)F_2上长为2~s的(1+u)-常循环码的距离分布

The Distributions of Distances of (1+u)-Constacyclic Codes of Length 2~s over F_2+uF_2+…+u^(k-1)F_2

研究码字的距离分布是编码理论的一个重要研究方向。该文定义了环R=F2+uF2++uk-1F2上的Homogeneous重量,研究了环R上长为2s的(1+u)-常循环码的Hamming距离和Homogeneous距离。使用了有限环和域的理论,给出了环R上长为2s的(1+u)-常循环码和循环自对偶码的结构和码字个数。并利用该常循环码的结构,确定了环R上长为2s的(1+u)-常循环码的Hamming距离和Homogeneous距离分布。

In coding theory, it is important to study the distance distribution of codewords. The Homogeneous weight over ring R=F2＋uF2＋…＋u^k-1F2 is defined. Hamming distances and Homogeneous distances of （1 ＋ u）- constacyclic codes of length 2^s over the ring R are studied. By means of the theory of finite rings, the structure of （1 ＋ u）- constacyclic codes of length 2^s~ over R is also obtained. Especially, the structure and the size of cyclic self-dual codes over the ring are also given. Then, using the structure of such constacyclic codes, the distributions of the Hamming distances and Homogeneous distances of such constacyclic codes are determined.