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Ranks of propelinear perfect binary codes (1210.8253v1)
Published 31 Oct 2012 in math.CO, cs.IT, and math.IT
Abstract: It is proven that for any numbers n=2m-1, m >= 4 and r, such that n - log(n+1)<= r <= n excluding n = r = 63, n = 127, r in {126,127} and n = r = 2047 there exists a propelinear perfect binary code of length n and rank r.