A novel search method for large polarization kernels is proposed. The algorithm produces a kernel with given partial distances by employing the depth-first search combined with the computation of coset leaders weight tables and sufficient conditions of code non-equivalence. Using the proposed method, we improved all existing lower bounds on the maximum error exponent for kernels of size from 17 to 29. We also obtained kernels which admit low complexity processing by the recently proposed recursive trellis algorithm. Numerical results demonstrate the advantage of polar codes with the obtained kernels compared with shortened polar codes and polar codes with small kernels.

翻译：提出了一种针对大型极化核的新型搜索方法。该算法通过结合深度优先搜索、陪集首权重表计算以及码非等价性的充分条件，生成了具有给定部分距离的极化核。利用所提方法，我们改进了现有关于尺寸为17至29的极化核最大错误指数的所有下界。此外，我们还获得了能够通过近期提出的递归网格算法实现低复杂度处理的极化核。数值结果表明，与缩短极化码及采用小型极化核的极化码相比，使用所得极化核的极化码具有显著优势。