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Generalized bent functions and their Gray images. (English) Zbl 1409.11135
Duquesne, Sylvain (ed.) et al., Arithmetic of finite fields. 6th international workshop, WAIFI 2016, Ghent, Belgium, July 13–15, 2016. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 10064, 160-173 (2016).
Summary: In this paper we prove that generalized bent (gbent) functions defined on \(\mathbb {F}_2^n\) with values in \(\mathbb {Z}_{2^k}\) are regular, and show connections between the (generalized) Walsh spectrum of these functions and their components. Moreover, we analyze generalized bent and semibent functions with values in \(\mathbb {Z}_{16}\) in detail, extending earlier results on gbent functions with values in \(\mathbb {Z}_4\) and \(\mathbb {Z}_8\).
For the entire collection see [Zbl 1358.11011].

11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
11T06 Polynomials over finite fields
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
Full Text: DOI arXiv
[1] Carlet, C.: \[ \mathbb{Z}_{2^k} \] -linear codes. IEEE Trans. Inf. Theory 44(4), 1543–1547 (1998) · Zbl 0935.94028
[2] Hodžić, S., Pasalic, E.: Generalized bent functions-some general construction methods and related necessary and sufficient conditions. Crypt. Commun. 7, 469–483 (2015) · Zbl 1343.94064
[3] Liu, H., Feng, K., Feng, R.: Nonexistence of generalized bent functions from \[ \mathbb{Z}_2^n \] to \[ \mathbb{Z}_m \] . Des. Codes Crypt. 82, 647–662 (2017) · Zbl 1370.11137
[4] Martinsen, T., Meidl, W., Stănică, P.: Generalized bent functions and their Gray images. http://arxiv.org/pdf/1511.01438 · Zbl 1409.11135
[5] Martinsen, T., Meidl, W., Stănică, P.: Partial spread and vectorial generalized bent functions. Des.Codes Crypt. (2017, to appear) · Zbl 1408.94997
[6] Kumar, P.V., Scholtz, R.A., Welch, L.R.: Generalized bent functions and their properties. J. Comb. Theory - Ser. A 40, 90–107 (1985) · Zbl 0585.94016
[7] Schmidt, K.U.: Quaternary constant-amplitude codes for multicode CDMA. IEEE Trans. Inform. Theory 55(4), 1824–1832 (2009) · Zbl 1367.94344
[8] Solé, P., Tokareva, N.: Connections between quaternary and binary bent functions. Prikl. Diskr. Mat. 1, 16–18 (2009). http://eprint.iacr.org/2009/544.pdf
[9] Stănică, P., Martinsen, T., Gangopadhyay, S., Singh, B.K.: Bent and generalized bent Boolean functions. Des. Codes Crypt. 69, 77–94 (2013) · Zbl 1322.94094
[10] Tan, Y., Pott, A., Feng, T.: Strongly regular graphs associated with ternary bent functions. J. Comb. Theory - Ser. A 117, 668–682 (2010) · Zbl 1267.05300
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