有限域上快速分块Jacket变换

Fast Construction of Block Jacket Transform over Finite Field

提出了一种在有限域上的简单上闭链分块逆Jacket变换(CBIJT)。为将高阶的上闭链逆Jacket矩阵(CBIJM)因式分解成单位矩阵和低阶稀疏矩阵,考虑运用带来快速变换的连续结构来减少计算负荷。采用类似的递归方式分析两个CBIJT,即单维和双维CBIJT。这两个CBIJT为单位矩阵和低阶CBIJT的多重Kronecker积。

We constructed anovel cocyclic block-wise inverse Jacket transform（CBIJT）with a fast transform.To factorize the large-size cocyclic block-wise inverse Jacket matrix（CBIJM）into several low-orderidentitymatrices and sparse matrices,we achieved a successive architecture that leads to a fast transform while reducing computational load.Two kinds of the CBIJTs,named one-dimensional and two dimensional CBIJTs,were designed with a similar recursive fashion,which refers the above-mentioned multi-fold product of identity matrices and CBIJTs.