On Z_4-Linear Goethals Codes and KloostermanSums

Authors:
Tor Helleseth;Victor Zinoviev
Affiliations:
Department of Informatics, University of Bergen, N-5020 Bergen, Noray;Institute for Problems of Information Transmission of the Russian Academy of Sciences, Bol‘shoi Karetnyi per. 19, GSP-4, Mosco, 101447, Russia
Venue:
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Year:
1999

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Abstract

Studying the coset weightdistributions of the Z_4-linear Goethals codes,e connect these codes with the Kloosterman sums. From one side,e obtain for some cases, of the cosets of weight four, the exactexpressions for the number of code ords of weight four in termsof the Kloosterman sums. From the other side, e obtain somelimitations for the possible values of the Kloosterman sums,hich improve the well known results due to Lachaud and Wolfmannkn:lac.