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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机译：根据Calderbank，McGuire，Kumar和Helleseth的论文（同上，第42卷，第1期，第217-26页，1996年1月），我们证明了以下结果：对于任何给定的正整数l / spl ges / 3，长度为2 / sup m / -1和设计距离2 / sup l / -1的二进制原始BCH码的Hensel提升的最小Lee权重（至Z / sub 4 /）仅为2 / sup l /当（a）m可以除以l或（b）m时的-1足够大。对于任意设计距离/ spl delta // spl ges / 4的二进制基本BCH码的Hensel提升，我们还证明了它们的最小Lee权重d / sub L // spl les / 2（[log / sub 2 // spl delta /] + 1）-1，当m足够大时。此外，证明了关于由Galois环定义的某些Z / sub 4 /码的最小Lee权重的结果，类似于Calderbank等人的结果。
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