关于二元等重码的最大码字数

本文利用Johnson Schemes理论研究了二元等重码及其最大码字数问题.在Delsarte的associate schemes理论中,Q-变换被引入以研究二元等重码的距离分布.首先,本文研究了等重码距离分布的Q-变换;然后,通过使用Q-变换的性质,我们研究了二元等重码的最大码字数问题并得到码字数的一个新的上界,该上界在形式上类似于纠错码理论中的Grey-Rankin界,并且在某些情况下优于已知的结果.

On the Maximum Number of Codewords of Binary Constant Weight Codes

The problems of maximum number of codewords for binary constant weight codes are studied by(employing) the theory of Johnson Schemes.In Delsarte's association schemes theory,Q-transform were introduced to study the distance distributions of binary constant weight codes.First,we study the Q-transforms of distance distributions of binary constant weight codes.Then,by using the properties of Q-transforms,we obtain a new upper bound of number of codewords for binary constant weight codes.This bound is similar to Grey-Rankin bound in error-correcting codes theory in form and improves previously known results in certain cases.