Codebooks from generalized bent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e146" altimg="si4.svg"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:math>-valued quadratic forms

Qi, Yanfeng; Mesnager, Sihem; Tang, Chunming

doi:10.1016/j.disc.2019.111736

Cited by 3 publications

(3 citation statements)

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“…In this paper, we proposed several classes of generalized bent functions and obtained codebooks nearly achieving the Welch bound. The generalized bent functions, as well as the parameters of the codebooks, constructed in this paper are different from those in [23].…”

Section: Codebooks From the Fourth Class Of Generalized Bent Functionsmentioning

confidence: 99%

“…Note that based on the theory of Z 4 -valued quadratic forms, the codebooks in [23] and this paper are both obtained by employing Heng and Yue's construction. In [23], Qi, Mesnager and Tang presented a class of generalized bent functions which generalizes Heng and Yue's functions, and derived codebooks meeting the Levenshtein bound. In this paper, we proposed several classes of generalized bent functions and obtained codebooks nearly achieving the Welch bound.…”

Section: Codebooks From the Fourth Class Of Generalized Bent Functionsmentioning

confidence: 99%

“…The constructions of codebooks meeting the Welch bound or the Levenshtein bound (optimal codebooks) have attracted much attention [5,6,8,12,23,26,30,32,33,38]. In general it is extremely hard to construct optimal codebooks [26].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nearly optimal codebooks from generalized Boolean bent functions over $ \mathbb{Z}_{4} $

Zhou¹,

Xu²,

Wang³

et al. 2022

AMC

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<p style='text-indent:20px;'>In this paper, based on the theory of <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{Z}_{4} $\end{document}</tex-math></inline-formula>-valued quadratic forms we propose several classes of generalized Boolean bent functions over <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{Z}_{4} $\end{document}</tex-math></inline-formula>, and new families of codebooks are constructed from these functions. The codebooks constructed in this paper are nearly optimal with respect to the Welch bound, and their parameters are new. Furthermore, some Boolean bent functions are also derived.</p>

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Section: Codebooks From the Fourth Class Of Generalized Bent Functionsmentioning

confidence: 99%

Section: Codebooks From the Fourth Class Of Generalized Bent Functionsmentioning

confidence: 99%