مرکز منطقه ای اطلاع رساني علوم و فناوري - On the inequivalence of generalized Preparata codes

DocumentCode :

936520

Title :

On the inequivalence of generalized Preparata codes

Author :

Kantor, William M.

Volume :

Issue :

fYear :

1983

fDate :

5/1/1983 12:00:00 AM

Firstpage :

345

Lastpage :

348

Abstract :

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.