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    Weighted Posets and Digraphs Admitting the Extended Hamming Code to be a Perfect Code

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    Recently, Etzion et al. introduced metrics on F-2(n) based on directed graphs on n vertices and developed some basic coding theory on directed graph metric spaces. In this paper, we consider the problem of classifying directed graphs, which admit the extended Hamming codes to be a perfect code. We first consider weighted poset metrics as a natural generalization of poset metrics and investigate interrelation between the weighted poset metrics and the directed graph-based metrics. In the next, we classify weighted posets on a set with eight elements and directed graphs on eight vertices, which admit the extended Hamming code (H) over tilde (3) to be a two-perfect code. We also construct some families of such structures for any k >= 3, which can be viewed as generalizations of some results presented by Etzion et al. and Hyun and Kim. Those families enable us to construct packing or covering codes of radius 2 under certain maps.11Nsciescopu

    A new distortion measure for spectral quantization based on the LSF intermodel interlacing property

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    The line spectral frequencies (LSFs) extracted from successive analysis orders are interlaced with each other. This intermodel interlacing property gives a new relationship between the closeness of LSFs and their spectral sensitivities, which motivates a new weighting function for LSF distortion measurement. By applying this new weighting function to LSF quantization, we have achieved a significantly better performance than the conventional heuristic weighting functions in both clean and noise environments. In addition, the proposed weighting function gives better performance than the weighting function based on a high-rate approximation (Gardner weighting (GW)) [W.R. Gardner, B.D. Rao, IEEE Trans. Speech Audio Processing 3 (5) (1995) 367] in noise environments while their performances are comparable in clean environments. Moreover, the complexity of the proposed weighting function is much lower than that of the GW function. (C) 2001 Elsevier Science B.V. All rights reserved.
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