On minimum Lee weights of Hensel lifts of some binary BCH codes

Motivated by the paper of Calderbank, McGuire, Kumar, and Helleseth (see ibid., vol.42, no.1, p.217-26, Jan. 1996) we prove the following result: for any given positive integer l⩾3, the minimum Lee weights of Hensel lifts (to Z₄) of binary primitive BCH codes of length 2^m-1 and designed distance 2^l-1 is just 2^l-1 when (a) m can be divided by l or (b) m is sufficiently large. For Hensel lifts of binary primitive BCH codes of arbitrary designed distance δ⩾4, we also prove that their minimum Lee weight d_L⩽2([log₂δ]+1)-1 when m is sufficiently large. Moreover, a result about minimum Lee weights of certain Z₄ codes defined by Galois rings, which is similar to the result in Calderbank et al., is proved