Constructing Generalized Bent Functions from Trace Forms of Galois Rings

Xiaoming Zhang (), Baofeng Wu (), Qingfang Jin () and Zhuojun Liu ()
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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

A chapter in Computer Mathematics, 2014, pp 467-477 from Springer

Abstract: 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.

Keywords: Galois Rings; Bent Property; Codeword; Permutation Polynomial; Monic Basic Irreducible Polynomial (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-662-43799-5_31

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