Abstract
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/spl ges/3, the minimum Lee weights of Hensel lifts (to Z/sub 4/) of binary primitive BCH codes of length 2/sup m/-1 and designed distance 2/sup l/-1 is just 2/sup 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 /spl delta//spl ges/4, we also prove that their minimum Lee weight d/sub L//spl les/2([log/sub 2//spl delta/]+1)-1 when m is sufficiently large. Moreover, a result about minimum Lee weights of certain Z/sub 4/ codes defined by Galois rings, which is similar to the result in Calderbank et al., is proved.
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