  Convolutional precoding in polarization-adjusted convolutional (PAC) codes
can reduce the number of minimum weight codewords (a.k.a error coefficient) of
polar codes. This can result in improving the error correction performance of
(near) maximum likelihood (ML) decoders such as sequential decoders and sphere
decoders. However, PAC codes cannot be decoded by sphere decoding. The reason
is twofold: 1) Sphere decoding of polar codes is performed from the last bit -
due to the lower rectangular shape of the polar transform. Whereas the shape of
PAC codes generator matrix is no longer triangular. 2) One may modify the
precoding matrix to get a lower-triangular shape. However, this may reduce the
minimum distance of the code due to the formation of unwanted cosets. This work
proposes a selective convolutional precoding scheme with transposed precoding
matrix to reduce the error coefficient while avoiding the reduction in the
minimum distance. The numerical results show the improvement of block error
rate by 0.2-0.6 dB, depending on the code rate, in medium and high SNR regimes.
