一种构造性证明不存在线性[90,78,5]_2码的方法

A constructive proof for the inexistence of linear[90,78,5]_2 code

针对判定线性码[90,78,5]_2的存在性问题,避开高维生成矩阵的构造问题,通过构造2个特殊的集合,采用集合覆盖的方法,进一步从2个方面分别计算2个构造集合中元素的数量,从中找出矛盾,进而证明了二元线性纠错码[90,78,5]_2不存在。根据最优线性码的定义可知,[90,78,4]_2是最优线性码。

To determine the existence problem of the linear[90,78,5]2 code,avoid high dimensional problems in the construction of the generator matrix,by constructing two special collections,the method of set covering further from two aspects respectively was used to calculate the amount of two structure elements in the collection and find contradiction.The results show that the binary linear error correcting[90,78,5]2 code does not exist.According to the definition of the optimal linear code,[90,78,4]2 is the optimal linear code.