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

In this paper, we use linear codes to study zero-error Slepian-Wolf coding of a set of sources with deviation symmetry, where the sources are generalization of the Hamming sources over an arbitrary field. We extend our previous codes, Generalized Hamming Codes for Multiple Sources, to Matrix Partition Codes and use the latter to efficiently compress the target sources. We further show that ever...

The Hamming distance is commonly used in the segmentation literature to measure the pixel-wise difference between two binary maps where 0 implies the two completely overlap. Here, we employ the Hamming distance metric to measure both the pixel-level accuracy and confidence of each pixel (close to 0 or 1). The smaller the Hamming distance, the more accurate is the model. In addition, we also com...

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...

This paper contains results on the generalized Hamming weights for the Goethals and Preparata codes over Z 4 : We give an upper bound on the rth generalized Hamming weights d r (m; j) for the Goethals code G m (j) of length 2 m over Z 4 , when m is odd. We also determine d 3:5 (m; j) exactly. The upper bound is shown to be tight up to r = 3:5. Furthermore we determine the rth generalized Hammin...

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...

Computing genetic evolution distances among a set of taxa dominates the running time of many phylogenetic inference methods. Most of genetic evolution distance definitions rely, even if indirectly, on computing the pairwise Hamming distance among sequences or profiles. We propose here an average-case linear-time algorithm to compute pairwise Hamming distances among a set of taxa under a given H...

Usually the mel-frequency cepstral coefficients (MFCCs) are derived via Hamming windowed DFT spectrum. In this paper, we advocate to use a so-called multitaper method instead. Multitaper methods form a spectrum estimate using multiple window functions and frequency-domain averaging. Multitapers provide a robust spectrum estimate but have not received much attention in speech processing. Our spe...

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...

In this paper, a generalization of Lucas addition chains, where subtraction is allowed, is given. It is called ”Lucas addition-subtraction chain” (LASC). LASC gives minimal addition-subtraction chains for infinitely many integers and will also be used to prove the optimality of Lucas addition chains for many cases. One of the main result in the theory of addition-subtraction chains is due to Vo...