In this note we consider the properties of the Hamming distance in combinatorial optimization problems on hypergraph matchings, also known as multidimensional assignment problems. It is shown that the Hamming distance between feasible solutions of hypergraph matching problems can be computed as an optimal value of linear assignment problem. For random hypergraph matching problems, an upper boun...

Given an arbitrary (nondeterministic) finite state automaton A we consider the problem of computing the Hamming distance of the language L(A) that is accepted by the automaton. This quantity is simply the minimum Hamming distance between any pair of distinct words from the language L(A). We show an algorithm that solves the problem in time quadratic with respect to the size of the given automat...

The minisum and the minimax rules are two different rules for the election of a committee considered by Brams et al. [2]. As input they assume approval ballots from the voters. The first rule elects those committees which minimize the sum of the Hamming distances to the votes, the second one elects those committees with the smallest maximum Hamming distance to an individual vote. We extend this...

A sequence of binary words of length n is called a cube dominating path, if the Hamming distance between two consecutive words is always one, and every binary word of length n is within Hamming distance one from at least one of these words. If also the first and last words are Hamming distance one apart, the sequence is called a cube dominating cycle. Bounds on the cardinality of such sequences...

We derive new estimates of the size of codes and orthogonal arrays in the ordered Hamming space (the Niederreiter-Rosenbloom-Tsfasman space). We also show that the eigenvalues of the ordered Hamming scheme, the association scheme that describes the combinatorics of the space, are given by the multivariate Krawtchouk polynomials, and establish some of their properties. CONTENTS

A weighted Hamming metric is introduced in [4] and it showed that the binary generalized Goppa code is a perfect code in some weighted Hamming metric. In this paper, we study the weight structures which admit the binary Hamming code and the extended binary Hamming code to be perfect codes in the weighted Hamming metric. And, we also give some structures of a 2-perfect code and how to construct ...

We consider dynamic and online variants of 2D pattern matching between an m×m pattern and an n× n text. All the algorithms we give are randomised and give correct outputs with at least constant probability. – For dynamic 2D exact matching where updates change individual symbols in the text, we show updates can be performed in O(log n) time and queries in O(log m) time. – We then consider a mode...

The class of the binary generalized Goppa codes is offered. It is shown that the codes of this class are on the Hamming bound constructed for a weighted metric.

For a Type T ∈ {I, II, III, IV} and length N where there exists no self-dual Type T code of length N , upper bounds on the minimum weight of the dual code of a self-orthogonal Type T code of length N are given, allowing the notion of dual extremal codes. It is proven that the Hamming weight enumerator of a dual extremal maximal self-orthogonal code of a given length is unique.

In this paper, we introduce generalized extended Hamming codes over Galois rings GR(2,m) of characteristic 2 with extension degree m. Furthermore we prove that the minimum Hamming weight of generalized extended Hamming codes over GR(2,m) is 4 and the minimum Lee weight of generalized extended Hamming codes over GR(8,m) is 6 for all m ≥ 3. ——————————————————————– ———Received May 25, 2011. This w...