New results on vectorial dual-bent functions and partial difference sets

Constructions of linear codes with two or three weights from vectorial dual-bent functions

“…By Corollary 2 and Proposition 5 of [5], F * (0) = F (0). Then the result follows from Proposition 4 of [36] and Lemma 1.…”

“…Proof. By Proposition 4 of [36] and its proof, F (x) − F (0) is a vectorial dual-bent function with Condition I, and the corresponding vectorial dual is F * (x) − F (0). By Corollary 2 and Proposition 5 of [5], F * (0) = F (0).…”

“…In the following, by the results in [7], [36] and Lemma 3, we list some explicit classes of vectorial dual-bent functions with Condition I.…”

“…Let F n q be the vector space of the n-tuples over the finite field F q , where q is a power of a prime p. A q-ary [n, k] linear code is a subspace of F n q with dimension k. Linear codes play an important role in coding theory. Among the known methods to construct linear codes, one of which is based on cryptographic functions, such as p-ary bent functions [10], [11], [19], [28], [31], [33], [40], [41], [43], [45], vectorial bent functions [2], [15], [21], [37], [39], [42], [44],…”

“…In [38], Wang and Heng utilized two classes of non-degenerate quadratic forms to construct qary self-orthogonal codes. By the results in [4], [35], [37], weakly regular p-ary bent functions of l-form with gcd(l − 1, p − 1) = 1 and non-degenerate quadratic forms with q being odd are actually vectorial dual-bent functions introduced in [7]. Hence, it is interesting to investigate whether there are general results on constructing self-orthogonal codes from vectorial dual-bent functions.…”