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On the inequivalence of generalized Preparata codes

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If m is odd and \sigma /\in Aut GF(2^{m}) is such that x \rightarrow x^{\sigma ^{2}-1} is 1-1 , there is a [2^{m+1}-1,2^{m+l}-2m-2] nonlinear binary code P(\sigma ) having minimum distance 5. All the codes P(\sigma ) have the same distance and weight enumerators as the usual Preparata codes (which rise as P(\sigma ) when x^{\sigma }=x^{2}) . It is shown that P(\sigma ) and P(\tau ) are equivalent if and only if \tau =\sigma ^{\pm 1} , and Aut P(\sigma ) is determined.

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Information Theory, IEEE Transactions on  (Volume:29 ,  Issue: 3 )