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http://dx.doi.org/10.4134/BKMS.b210183

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

Sankhadip, Roy (Department of Basic Science and Humanities University of Engineering and Management)
Publication Information
Bulletin of the Korean Mathematical Society / v.59, no.6, 2022 , pp. 1327-1337 More about this Journal
Abstract
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.
Keywords
Zero-difference balanced (ZDB) function; cyclotomic polynomials; cyclotomic coset; constant composition code;
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