Abstract
Let H n be a Hadamard matrix of order n (see (1.3.5)). In H n and — H n we replace — 1 by 0. In this way we find 2n rows which are words in F n2 . Since any two rows of a Hadamard matrix differ in half of the positions we have constructed an (n, 2n, \( \frac{1}{2} \) n) code. For n = 8 this is an extended Hamming code. For n = 32 the code is the one used by Mariner 1969 which was mentioned in Section 2.1. In general these codes are called Hadamard codes.
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© 1999 Springer-Verlag Berlin Heidelberg
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van Lint, J.H. (1999). Some Good Codes. In: Introduction to Coding Theory. Graduate Texts in Mathematics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58575-3_4
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DOI: https://doi.org/10.1007/978-3-642-58575-3_4
Publisher Name: Springer, Berlin, Heidelberg
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