二元最优自正交［15s+10,4］码的分类

自正交码是一类重要的纠错码,其中的特殊类型——自对偶码一直是研究的重点。研究二元域码长为n=15s 10(s≥0)的四维最优自正交码的特征,并且确定其完整分类。建立了最优15s 10,4]自正交码的生成矩阵与两个线性方程组之间的联系,将确定最优15s 10,4]自正交码的问题转化为求解线性方程组的问题。确定出所有最优15s 10,4]自正交码的生成矩阵,并进一步得到互不等价的最优自正交码的完整分类,给出了互不等价且不含全零坐标的最优15s 10,4]自正交码的生成矩阵和重量多项式。因此,二元域上最优15s 10,4]自正交码的参数、结构特征和等价问题得到了完全解决。

Classification of Binary Optimal Self-orthogonal Codes

The complete classification of 4-dimensional optimal self-orthogonal codes of code length is presented.The establishment of the optimal orthogonal code matrix and the formation of linear equations between the two links will determine the problem of optimal orthogonal code transforming into that of solving linear equations.Results identify all generator matrixes of the optimal orthogonal code,and further are not equivalent to the optimal orthogonal codes since the integrity of classification,and the generator matrices and weight polynomials of these 4-dimensional optimal self-orthogonal codes are also given.Therefore,the optimal orthogonal code parameters,structural characteristics and equivalence problem have been completely solved.