We study formulae to count the number of binary vectors of length n that are linearly independent k at a time where n and k are given positive integers with 1 ≤ k ≤ n. Applications are given to the design of hypercubes and orthogonal arrays, pseudo (t, m, s)-nets and linear codes. 1991 AMS(MOS) Classification: Primary: 11T30; secondary: 05B15.

A new class of pseudo-random sequences (called cascaded GMW-type permutation polynomial (CGPP) sequences) over GF (qn) is constructed using a system of n orthogonal cascaded GMW functions in GF (q). Their statistical properties are given. Classification, evaluation, and implementation of the CGPP sequences are derived. A sequence generated by mapping elements of a CGPP sequence into GF (q) is a...

We study a new variant of colored orthogonal range searching problem: given a query rectangle Q all colors c, such that at least a fraction τ of all points in Q are of color c, must be reported. We describe several data structures for that problem that use pseudo-linear space and answer queries in poly-logarithmic time.

By studying quantum information masking in non-Hermitian systems, we show that mutually orthogonal states can be deterministically masked, while an arbitrary set of cannot masked systems. We further demonstrate a linearly independent which are $\eta$-orthogonal by pseudo-unitary operator. Moreover, study robustness against noisy environments. The deterministic and probabilistic under different ...

In a recent article, the first and second kinds of multivariate Chebyshev polynomials fractional degree, relevant integral repesentations, have been studied. this we introduce pseudo-Lucas functions show possible applications these new functions. For kind, compute Newton sum rules any orthogonal polynomial set starting from entries Jacobi matrix. representation formulas for powers r×r matrix, a...

SUMMARY In this paper, a new large spreading code set with a uniform low cross-correlation is proposed. The proposed code set is capable of (1) increasing the number of assigned user (capacity) in a multicarrier code division multiple access (MC-CDMA) system and (2) reducing the peak-to-average power ratio (PAPR) of an orthogonal frequency division multiplexing (OFDM) system. In this paper, we ...

The continuous orthogonal polynomials, such as Zernike and pseudo-Zernike, are often used as an expansion of corneal height data. However, the use of continuous polynomials has some limitations due to the discretization. It is because that the integrals are usually approximated by discrete summations, and this process not only leads to numerical errors, but also severely affects some analytical...

We consider pseudo-unitary quantum systems and discuss various properties of pseudounitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal blocks. Furthermore, we show that every pseudo-unitary matrix is the exponential of i = √ −1 times a pseudo-Hermitian matrix, and determine the structure of the L...