We present a N-dimensional generalization of the two-dimensional block-circulant perfect array construction by [Blake, 2013]. As in [Blake, 2013], the families of N-dimensional arrays possess pairwise good zero correlation zone (ZCZ) cross-correlation. Both constructions use a perfect autocorre-lation sequence with the array orthogonality property (AOP). This paper presents a generalization of ...

Properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16 Abstract. Some properties of perfect transitive binary codes of length 15 and extended perfect transitive binary codes of length 16 are presented for reference purposes. The attached files contain some tab-delimited properties of perfect binary codes of length 15 and extended per...

Functions with low differential uniformity have relevant applications in cryptography. Recently, functions c-differential attracted lots of attention. In particular, so-called APcN and PcN (generalization APN PN functions) been investigated. Here, we provide a characterization such via quadratic polynomials as well non-existence results.

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

For any 1-error-correcting binary code C of length m we will construct a 1-perfect binary code P (C) of length n = 2 − 1 such that fixing the last n − m coordinates by zeroes in P (C) gives C. In particular, any complete or partial Steiner triple system (or any other system that forms a 1-code) can always be embedded in a 1-perfect code of some length (compare with [13]). Since the weight-3 wor...

For a not empty perfect subset of the unit circle C there is a perfect subset of C measure zero which being rotated to every position intersects the first set on a nonempty perfect set. This result may be stated in terms of set of distances between pairs of points from these two sets. A generalization of this result to a product of tori is suggested. 2000 Mathematics Subject Classification: 26-...

A new family of chiral ferrocenyl P,S-ligands has been developed and successfully applied in a highly endo-selective catalytic asymmetric cycloaddition of azomethine ylides with various enones, including cyclic and acyclic α-enones. For cyclic α-enones, a [Cu(CH(3)CN)(4)]ClO(4)/(R(c),S(Fc))-2f complex catalyzed the cycloaddition to give the sole endo-cycloadducts in perfect enantioselectivities...

Certain subgraphs of a given graph G restrict the minimum number χ(G) of colors that can be assigned to the vertices of G such that the endpoints of all edges receive distinct colors. Some of such subgraphs are related to the celebrated Strong Perfect Graph Theorem, as it implies that every graph G contains a clique of size χ(G), or an odd hole or an odd anti-hole as an induced subgraph. In thi...