New Kloosterman sum identities from the Helleseth-Zinoviev result on Z_4-linear Goethals codes

04/02/2019

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by   Minglong Qi, et al.

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In the paper of Tor Helleseth and Victor Zinoviev (Designs, Codes and Cryptography, 17, 269-288(1999)), the number of solutions of the system of equations from Z_4 -linear Goethals codes G_4 was determined and stated in Theorem 4. We found that Theorem 4 is wrong for m even. In this note, we complete Theorem 4, and present a series of new Kloosterman sum identities deduced from Theorem 4. Moreover, we show that several previously established formulas on the Kloosterman sum identities can be rediscovered from Theorem 4 with much simpler proofs.