%0 Journal Article
%T On the Construction of the Kernel Matrix by Primitive BCH Codes for Polar Codes
%A Liping Lin
%J Communications and Network
%P 23-35
%@ 1947-3826
%D 2022
%I Scientific Research Publishing
%R 10.4236/cn.2022.141003
%X The polar codes defined by the kernel matrix are a class of codes with low coding-decoding complexity and can achieve the Shannon limit. In this paper, a novel method to construct the 2<sup>n</sup>-dimensional kernel matrix is proposed, that is based on primitive BCH codes that make use of the interception, the direct sum and adding a row and a column. For ensuring polarization of the kernel matrix, a solution is also put forward when the partial distances of the constructed kernel matrix exceed their upper bound. And the lower bound of exponent of the 2<sup>n</sup>-dimensional kernel matrix is obtained. The lower bound of exponent of our constructed kernel matrix is tighter than Gilbert-Varshamov (G-V) type, and the scaling exponent is better in the case of 16-dimensional.
%K Polar Code
%K Kernel Matrix
%K Matrix Interception
%K Partial Distance
%K Exponent
%K Scaling Exponent
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=114763