Finite fields
Fast Algorithms for Determining the Linear Complexity of Period Sequences
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
A New Characterization of Semi-bent and Bent Functions on Finite Fields*
Designs, Codes and Cryptography
Designs, Codes and Cryptography
Construction of bent functions from near-bent functions
Journal of Combinatorial Theory Series A
A construction of weakly and non-weakly regular bent functions
Journal of Combinatorial Theory Series A
A fast algorithm for determining the linear complexity of a sequence with period pn over GF(q)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Shift-register synthesis and BCH decoding
IEEE Transactions on Information Theory
A fast algorithm for determining the complexity of a binary sequence with period (Corresp.)
IEEE Transactions on Information Theory
Fast algorithms for determining the linear complexity of sequences over GF(pm) with period 2tn
IEEE Transactions on Information Theory
On bent and semi-bent quadratic Boolean functions
IEEE Transactions on Information Theory
Trace forms over finite fields of characteristic 2 with prescribed invariants
Finite Fields and Their Applications
Highly degenerate quadratic forms over finite fields of characteristic 2
Finite Fields and Their Applications
Bent Functions of Maximal Degree
IEEE Transactions on Information Theory
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We study a class of quadratic p-ary functions $${{\mathcal{F}}_{p,n}}$$ from $${\mathbb{F}_{p^n}}$$ to $${\mathbb{F}_p, p \geq 2}$$ , which are well-known to have plateaued Walsh spectrum; i.e., for each $${b \in \mathbb{F}_{p^n}}$$ the Walsh transform $${\hat{f}(b)}$$ satisfies $${|\hat{f}(b)|^2 \in \{ 0, p^{(n+s)}\}}$$ for some integer 0 驴 s 驴 n 驴 1. For various types of integers n, we determine possible values of s, construct $${{\mathcal{F}}_{p,n}}$$ with prescribed spectrum, and present enumeration results. Our work generalizes some of the earlier results, in characteristic two, of Khoo et. al. (Des Codes Cryptogr, 38, 279---295, 2006) and Charpin et al. (IEEE Trans Inf Theory 51, 4286---4298, 2005) on semi-bent functions, and of Fitzgerald (Finite Fields Appl 15, 69---81, 2009) on quadratic forms.