On the variance of average distance of subsets in the Hamming space

Autor:	Chaoping Xing, San Ling, Fang-Wei Fu
Přispěvatelé:	School of Physical and Mathematical Sciences
Rok vydání:	2005
Předmět:	Combinatorics Cardinality Applied Mathematics Value (computer science) Discrete Mathematics and Combinatorics Hamming distance Coding theory Variance (accounting) Hamming space Upper and lower bounds Finite set Science::Mathematics::Discrete mathematics [DRNTU] Mathematics
Zdroj:	Discrete Applied Mathematics. 145(3):465-478
ISSN:	0166-218X
DOI:	10.1016/j.dam.2004.08.004
Popis:	Let V be a finite set with q distinct elements. For a subset C of V n, denote var(C) the variance of the average Hamming distance of C. Let T (n,M; q) and R(n,M; q) denote the minimum and maximum variance of the average Hamming distance of subsets of V n with cardinality M, respectively. In this paper, we study T (n,M; q) and R(n,M; q) for general q. Using methods from coding theory, we derive upper and lower bounds on var(C), which generalize and unify the bounds for the case q = 2. These bounds enable us to determine the exact value for T (n,M; q) and R(n,M; q) in several cases. Accepted version
Databáze:	OpenAIRE
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