Preparata code: Difference between revisions

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Revision as of 11:24, 1 July 2014

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==Construction==

Let ''m'' be an odd number, and ''<math>n'' = 2<sup>''^m''-1</supmath>&nbsp;&minus;&nbsp;1. We first describe the '''extended Preparata code''' of length 2''n''&nbsp;<math>2n+&nbsp;2 = 2<sup>''^{m''&nbsp;+&nbsp;1}</supmath>: the Preparata code is then derived by deleting one position. The words of the extended code are regarded as pairs (''X'',&nbsp;''Y'') of 2^''m''-tuples, each corresponding to subsets of the [[finite field]] GF(2^''m'') in some fixed way.

The extended code contains the words (''X'',&nbsp;''Y'') satisfying three conditions