 
Summary: PERGAMON
An InternationalJournal
computers &
mathematics
with applications
Computers and Mathematics with Applications 39 (2000) 129134
www.elsevier,nl/locate/camwa
Maximal Codeword Lengths
in Huffman Codes
Y. S. ABUMOSTAFA AND R. J. MCELIECE
Department of Electrical Engineering, California Institute of Technology
MS 13693, Pasadena, CA 91125, U.S.A.
In celebration of the 60th birthday of Solomon W. Golomb
AbstractIn this paper, we consider the following question about Huffman coding, which is
an important technique for compressing data from a discrete source. If p is the smallest source
probability, how long, in terms of p, can the longest Huffman codeword be? We show that if p is
in the range 0 < p <_ 1/2, and if K is the unique index such that 1/F/¢+3 < p < 1/FK+2, where
FK denotes the K th Fibonacci number, then the longest Huffman codeword for a source whose least
probability is p is at most K, and no better bound is possible. Asymptotically, this implies the
surprising fact that for small values of p, a Huffman code's longest codeword can be as much as
