Title :
A Bound on Equitable Partitions of the Hamming Space
Author_Institution :
Dept. of Math., Ewha Womans Univ., Seoul, South Korea
fDate :
5/1/2010 12:00:00 AM
Abstract :
We denote Qn the set of binary words of length n. A partition {C1,C2,¿,Cr} of Qn with quotient matrix B = (bij)r×r is equitable if for all i and j, any word in d has exactly bij neighbors in Cj. The equitable partitions of Qn can be obtained from completely regular codes. We derive a bound on equitable partitions of Qn that does not depend on the size of the partition.
Keywords :
Hamming codes; binary codes; matrix algebra; Hamming space; binary words; equitable partitions; quotient matrix; regular codes; Codes; Educational programs; Educational technology; Eigenvalues and eigenfunctions; Hamming distance; Labeling; Mathematics; Polynomials; Completely regular code; correlation immune function; equitable partition; perfect coloring;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2043773
