In this paper, we investigate properties of generalized bent Boolean functions and 2k-bent (i.e., negabent, octabent, hexadecabent, et al.) in a uniform framework. From the Hadamard matrices, Hodzic Pasalic presented sufficient conditions for functions. Using cyclotomic fields decomposition functions, generalize their results, prove that Pasalic's are not only but also necessary, completely characterize terms component Furthermore, present secondary construction or semibent from Finally,...

In this paper, a generic construction of codebooks based on binary codes is introduced. With construction, few previous constructions optimal are extended, and new class almost meeting the Levenshtein bound presented. Exponentially many or from obtained in paper. The constructed paper have alphabet size 4. As byproduct, three bounds parameters derived.

Linear codes generated by component functions of perfect nonlinear (PN for short) and almost (APN the first-order Reed-Muller have been an object intensive study in coding theory. The objective this paper is to investigate some binary shortened two families linear from APN <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> -ary associated with PN functions. weight distributions...

Linear codes are widely employed in communication systems, consumer electronics, and storage devices. All linear over finite fields can be generated by a generator matrix. Due to this, the matrix approach is called fundamental construction of codes. This only known method that produce all fields. Recently, defining-set has attracted lot attention, have been huge number classes It was claimed this also generate But so far, no proof claim given literature. The objective paper prove claim,...

The traditional algorithm for smoothing fingerprint orientation fields was based on the low-pass filter. To improve this algorithm, a variable window adaptive is proposed consistency. Our uses correctness of field to compute weighted average field. Experiments show that our can effectively deal with images which have noises and really describe topological structure ridge.

In this paper, we present a construction of linear codes over F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2t</sub> from Boolean functions, which is generalization Ding's method. Based on construction, give two classes C̃ xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> and C function f : xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> → xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , where q = 2 <sup...

In this paper, we present a construction of linear codes over $\f_{2^t}$ from Boolean functions, which is generalization Ding's method \cite[Theorem 9]{Ding15}. Based on construction, give two classes $\tilde{\C}_{f}$ and $\C_f$ (see Theorem \ref{thm-maincode1} \ref{thm-maincodenew}) function $f:\f_{q}\rightarrow \f_2$, where $q=2^n$ some subfield $\f_{q}$. The complete weight enumerator can be easily determined the Walsh spectrum $f$, while distribution code also settled. Particularly,...

Linear codes generated by component functions of perfect nonlinear (PN) and almost (APN) the first-order Reed-Muller have been an object intensive study in coding theory. The objective this paper is to investigate some binary shortened two families linear from APN $p$-ary associated with PN functions. weight distributions these parameters their duals are determined. flexible. Many presented optimal or optimal. results show that shortening technique very promising for constructing good codes.

&lt;p style='text-indent:20px;'&gt;In this paper, we present two constructions of low-hit-zone frequen-cy-hopping sequence (LHZ FHS) sets. The in paper generalize the previous based on &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ m $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-sequences and id="M2"&gt;\begin{document}$ d $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-form functions with difference-balanced property, generate several classes optimal LHZ...

Linear codes can be employed to construct authentication codes, which is an interesting area of cryptography. The parameters the depend on complete weight enumerator underlying linear codes. In order obtain code with good parameters, must have proper parameters. first objective this paper determine enumerators a class two weights and three weights. second employ these new

A generic construction of linear codes over finite fields has recently received a lot attention, and many one-weight, two-weight three-weight with good error correcting capability have been produced this approach. The first objective paper is to establish relationships among some classes obtained approach, so that the parameters can be derived from those other known parameters. In way, new will derived. second present class binary consider their applications in secret sharing.