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

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 pa...

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محفوظ في:
التفاصيل البيبلوغرافية
المؤلفون الرئيسيون: Fu, Fang-Wei, Ling, San, Xing, Chaoping
مؤلفون آخرون: School of Physical and Mathematical Sciences
التنسيق: مقال
اللغة:English
منشور في: 2013
الموضوعات:
الوصول للمادة أونلاين:https://hdl.handle.net/10356/96425
http://hdl.handle.net/10220/9840
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الوصف
الملخص: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.