Minimum average distance subsets in the hamming cube

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) andR(n,M; q) denote the minimum and maximum variance of the average Hamming distance of subsets of V n with cardinalityM, 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 up...

Minimum Average Distance Triangulations

Some of the following problems look similar to the MAD Triangulation problem, but we have not found any deep connections: •Minimum Average Distance Spanning Subgraph in a budgeted version [2] was studied in the context of network design (minimizing average routing time). The problem is NP-complete even with unit weights. •Minimum Average Distance Spanning Tree [1]. NP-completeness is implied by...

Using minimum degree to bound average distance

Total and average distance are not only interesting invariants of graphs in their own right but are also used for studying properties or classifying graphical systems that depend on the number of edges traversed. Recent examples include studies of computer networks [3] and the use of graphical invariants to partially classify the structure of molecules [1]. There have been a number of conjectur...

Design of Linear-phase Fir Filters with Minimum Hamming Distance

In this paper a new approach for the design of linear phase FIR filters with discrete coefficients is proposed. A mixed integer linear programming (MILP) problem is formulated that minimizes the total Hamming distance between the adjacent coefficients, i.e., the number of bit switches of the coefficients. The Hamming distance between the coefficients is a good measure of the power consumption, ...

Linear Binary Error Correcting Codes with Specified Minimum Hamming Distance