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1 Correction to: Adv. Appl. Clifford Algebras (2019) 29:93 https://doi.org/10.1007/s00006-019-1012-x
Remark 4.1 and Remark 4.5 in Section 4 will be true only if a is a power of two. Hence, the proofs of Theorem 4.2 and Theorem 4.6 hold in the case of a being a power of 2.
More generally, both Theorems 4.2 and 4.6 are true by observing the change of variable \(x \rightarrow y+1\) in the Walsh-Hadamard Transform, as it is a permutation on the finite field, i.e., we get exactly opposite values of the function \(f(x)=\mathrm {Tr}(x)^d\), where d is the Niho exponent. Since the function \(f(x)=\mathrm {Tr}(x)^d\) is near-bent function, the function \(f(x)=\mathrm {Tr}(x+1)^d\) is also a near bent function.
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The authors of this manuscript gratefully acknowledge the valuable advices and suggestions provided by Professor Samed Bajrić, Jozef Stefan Institute, Slovenia, to make this clarification.
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Poojary, P., Panackal, H. & Bhatta, V.G.R. Correction to: Algebraic Construction of Near-Bent and APN Functions. Adv. Appl. Clifford Algebras 30, 26 (2020). https://doi.org/10.1007/s00006-020-1051-3
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DOI: https://doi.org/10.1007/s00006-020-1051-3