  Polarization-adjusted convolutional (PAC) codes can approach the theoretical
bound for block error rate (BLER) performance at short-to-medium codeword
length. PAC codes have excellent BLER performance using Monte Carlo (MC)
rate-profiles and Weighted Sum (WS) rate-profiles, but the BLER performances of
the constructed codes still fall away from the dispersion bound at high
signal-to-noise ratios (SNR). This paper proposes a List-Search (LS)
construction method for PAC codes, which considers the influence of weight
spectrum on BLER performance and the condition that sequence decoding for PAC
codes having a finite mean computational complexity. The proposed construction
method using LS can reduce the number of minimum weight codewords of PAC codes.
The BLER performance of the constructed codes is better than that of the
constructed codes using MC rate-profiles or WS rate-profiles, and can approach
the dispersion bound at high SNR. Moreover, the BLER performance of successive
cancellation list (SCL) decoding PAC codes using LS rate-profiles can approach
the theoretical bound, but SCL decoding requires a large number of sorting
operations. To reduce the number of sorting operations, a path-splitting
critical sets (PSCS) construction method is proposed. The PSCS obtained by this
method are the information bits subset that have the greatest influence on the
number of minimum weight codewords. The simulation results show that this
method can significantly reduce the number of sorting operations during
SCL-type decoding.
