Lin, H.P., Lin, S. and Abdel-Ghaffar, K.A.S. (2015) Linear and Nonlinear Binary Kernels of Polar Codes of Small Dimensions with Maximum Exponents. IEEE Transactions on Information Theory, 61, 5253-5270.
https://doi.org/10.1109/TIT.2015.2469298

has been cited by the following article:

• TITLE: On the Construction of the Kernel Matrix by Primitive BCH Codes for Polar Codes

  AUTHORS: Liping Lin

  KEYWORDS: Polar Code, Kernel Matrix, Matrix Interception, Partial Distance, Exponent, Scaling Exponent

  JOURNAL NAME: Communications and Network, Vol.14 No.1, January 21, 2022

  ABSTRACT: 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 2n-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 2n-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.