Ranks of propelinear perfect binary codes
  It is proven that for any numbers n=2^m-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. 
George K. Guskov, Ivan Yu. Mogilnykh, Faina I. Solov'eva
math.CO cs.IT math.IT