• 제목/요약/키워드: zero-difference balanced (ZDB) function

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ON GENERALIZED ZERO-DIFFERENCE BALANCED FUNCTIONS

  • Jiang, Lin;Liao, Qunying
    • 대한수학회논문집
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    • 제31권1호
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    • pp.41-52
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    • 2016
  • In the present paper, by generalizing the definition of the zero-difference balanced (ZDB) function to be the G-ZDB function, several classes of G-ZDB functions are constructed based on properties of cyclotomic numbers. Furthermore, some special constant composition codes are obtained directly from G-ZDB functions.

SOME NEW CLASSES OF ZERO-DIFFERENCE BALANCED FUNCTIONS AND RELATED CONSTANT COMPOSITION CODES

  • Sankhadip, Roy
    • 대한수학회보
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    • 제59권6호
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    • pp.1327-1337
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    • 2022
  • Zero-difference balanced (ZDB) functions can be applied to many areas like optimal constant composition codes, optimal frequency hopping sequences etc. Moreover, it has been shown that the image set of some ZDB functions is a regular partial difference set, and hence provides strongly regular graphs. Besides, perfect nonlinear functions are zero-difference balanced functions. However, the converse is not true in general. In this paper, we use the decomposition of cyclotomic polynomials into irreducible factors over 𝔽p, where p is an odd prime to generalize some recent results on ZDB functions. Also we extend a result introduced by Claude et al. [3] regarding zero-difference-p-balanced functions over 𝔽pn. Eventually, we use these results to construct some optimal constant composition codes.