Abstract
Levenshtein described in [5] a method for constructing error correcting codes which meet the Plotkin bounds, provided suitable Hadamard matrices exist. Uncertainty about the existence of Hadamard matrices on all orders multiple of 4 is a source of difficulties for the practical application of this method. Here we extend the method to the case of quasi-Hadamard matrices. Since efficient algorithms for constructing quasi-Hadamard matrices are potentially available from the literature (e.g. [7]), good error correcting codes may be constructed in practise. We illustrate the method with some examples.
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Álvarez, V., Armario, J.A., Frau, M.D., Martin, E., Osuna, A. (2007). Error Correcting Codes from Quasi-Hadamard Matrices. In: Carlet, C., Sunar, B. (eds) Arithmetic of Finite Fields. WAIFI 2007. Lecture Notes in Computer Science, vol 4547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73074-3_23
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DOI: https://doi.org/10.1007/978-3-540-73074-3_23
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