Computational hardness assumption from the syndrome decoding problem has been useful in designing the security of code based cryptosystem that are safe against quantum computing. Due to complexities in solution using high degree linearized polynomial equations modeled from subspaces, we proposed exploiting the dependency between subspaces in a Grassmann graph constructed from Boundary measurement maps by using copula functions. We also used copula functions to estimate the marginal distribution in these subspaces. Thereafter, the Maximum likelihood based estimation approach was used to search the codeword that maximizes the conditional distribution and in the process approximate a solution to the problem. Results of the Bit Error Rate performance obtained from simulation shows that the proposed solution performs better than the information set decoding method.

翻译：从综合症解码问题中得出的计算硬度假设有助于设计基于代码的加密系统的安全性,这种加密系统对量计算是安全的。由于使用从子空间建模的高度线性多元方程式的解决方案的复杂性,我们建议利用从边界测量图中绘制的格拉斯曼图中的子空间之间的依赖性,使用 Coupula 函数来估计这些子空间的边际分布。随后,采用了基于最大可能性的估计方法来搜索使有条件分布最大化的代码,并在该过程中接近于解决问题的解决方案。从模拟中获得的比特错误率表现显示,拟议解决方案的表现优于信息集解码方法。