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Constructing Generalized Bent Functions from Trace Forms of Galois Rings

In: Computer Mathematics

Author

Listed:
  • Xiaoming Zhang

    (Chinese Academy of Science, Key Laboratory of Mathematics Mechanization, AMSS)

  • Baofeng Wu

    (Chinese Academy of Science, Key Laboratory of Mathematics Mechanization, AMSS)

  • Qingfang Jin

    (Chinese Academy of Science, Key Laboratory of Mathematics Mechanization, AMSS)

  • Zhuojun Liu

    (Chinese Academy of Science, Key Laboratory of Mathematics Mechanization, AMSS)

Abstract

Quaternary constant-amplitude codes (codes over $${\mathbb Z}_4$$ Z 4 ) of length $$2^m$$ 2 m exist for every positive integer $$m$$ m , and every codeword of such a code corresponds to a function from the binary $$m$$ m -tuples to $${\mathbb Z}_4$$ Z 4 having the bent property, called a generalized bent function. In this chapter, we extend previous constructions and propose a general approach which can lead to more generalized bent functions.

Suggested Citation

  • Xiaoming Zhang & Baofeng Wu & Qingfang Jin & Zhuojun Liu, 2014. "Constructing Generalized Bent Functions from Trace Forms of Galois Rings," Springer Books, in: Ruyong Feng & Wen-shin Lee & Yosuke Sato (ed.), Computer Mathematics, edition 127, pages 467-477, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-43799-5_31
    DOI: 10.1007/978-3-662-43799-5_31
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