Title :
Rank spectrum of propelinear perfect binary codes
Author :
Guskov, George K. ; Mogilnykh, Ivan Yu ; Solov´eva, Faina I.
Author_Institution :
Sobolev Inst. of Math., Novosibirsk, Russia
Abstract :
It is known [4] that for any numbers n = 2m - 1, m ≥ 4 and r, such that n - log(n + 1) ≤ r ≤ n there exists a perfect binary code of length n and rank r. We show that there exists a propelinear such code of length n, excluding, may be, n = r = 63, n = 127, r ϵ {126,127} and n = r = 2047.
Keywords :
binary codes; linear codes; code length; code rank; propelinear perfect binary code; rank spectrum; Binary codes; Electronic mail; Kernel; Propulsion; Vectors;
Conference_Titel :
Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on
Conference_Location :
Istanbul
DOI :
10.1109/ISIT.2013.6620352
