We give two new characterizations of pairs of polynomials or trigonometric polynomials that form a composition pair. One of them proves that the cancellation of a given number of double moments implies that they form a composition pair. This number only depends on the maximum degree of both polynomials. This is the first time that composition is characterized in terms of the cancellation of an ...

We give an exact characterization of permutation polynomials mod ulo n w w a polynomial P x a a x adx d with integral coe cients is a permutation polynomial modulo n if and only if a is odd a a a is even and a a a is even We also characterize polynomials de ning latin squares mod ulo n w but prove that polynomial multipermutations that is a pair of polynomials de ning a pair of orthogonal latin...

Sequences with good correlation properties have been widely adopted in modern communications, radar and sonar applications. In this paper, we present our new findings on some constructions of single H-ary Golay sequence and 4-QAM Golay complementary sequence with a large zero autocorrelation zone, where H ≥ 2 is an arbitrary even integer and q ≥ 2 is an arbitrary integer. Those new results on G...

We explicitly determine the defining relations of all quantum symmetric pair coideal subalgebras quantized enveloping algebras Kac-Moody type. Our methods are based on star products noncommutative $\mathbb{N}$-graded algebras. The resulting expressed in terms continuous q-Hermite polynomials and a new family deformed Chebyshev polynomials.

Let C be a binary self-dual code with an automorphism g of order 2p, where p is an odd prime, such that g is a xed point free involution. If C is extremal of length a multiple of 24 all the involutions are xed point free, except the Golay Code and eventually putative codes of length 120. Connecting module theoretical properties of a self-dual code C with coding theoretical ones of the subcode C...

Similar to algebraic decoding schemes, the (23, 12, 7) Golay code can be decoded by applying the step-by-step decoding algorithm. In this work, a modified step-by-step algorithm for decoding the Golay code is presented. Logical analysis yielded a simple rule for directly determining whether a bit in the received word is correct. The computational complexity can be reduced significantly using th...

This technical report addresses model-based interpolation of long signal gaps. It demonstrates that employing a modified autoregressive AR model, computed as a weighted sum of line spectral pair (LSP) polynomials, is more efficient computationally than using a conventional AR model, since longer signal gaps can be interpolated at reduced model order. Key-words: acoustic signal processing, audio...

One of the interesting features in the development of analysis in the twentieth century is the remarkable growth, in various directions, of the theory of orthogonal functions. Two brilliant achievements on the threshold of this century—Fejér's paper on Fourier series and Fredholm's papers on integral equations—have been acting as a powerful inspiring source of attraction, inviting analysts to d...

The pair of groups, symmetric group S2n and hyperoctohedral group Hn , form a Gelfand pair. The characteristic map is a mapping from the graded algebra generated by the zonal spherical functions of (S2n, Hn) into the ring of symmetric functions. The images of the zonal spherical functions under this map are called the zonal polynomials. A wreath product generalization of the Gelfand pair (S2n, ...

This paper discusses operators lowering or raising the degree but preserving the parameters of special orthogonal polynomials. Results for onevariable classical (q-)orthogonal polynomials are surveyed. For Jacobi polynomials associated with root system BC2 a new pair of lowering and raising operators is obtained.