Golay complementary sequences, often referred to as Golay pairs, are characterised by the property that the sum of their aperiodic autocorrelation functions equals to zero, except for the zero shift. Because of this property, Golay complementary sequences can be utilised to construct Hadamard matrices defining sets of orthogonal spreading sequences for DS CDMA systems of the lengths not necessa...

We give explicit combinatorial product formulas for the polynomials encoding the dimensions of the spaces of extensions of (g, p)-generalized Verma modules, in the cases when (g, p) corresponds to an indecomposable classic Hermitian symmetric pair. The formulas imply that these dimensions are combinatorial invariants. We also discuss how these polynomials, defined by Shelton, are related to the...

Formulae expressing explicitly the coefficients of an expansion of double Jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. Extension to expansion of triple Jacobi polynomials is given. The results for the special cases of double and triple ultraspher...

Sequences with zero autocorrelation are of interest because of their use in constructing orthogonal matrices and because of applications in signal processing, range finding devices, and spectroscopy. Golay sequences, which are pairs of binary sequences (i.e., all entries are \1) with zero autocorrelation, have been studied extensively, yet are known only in lengths 21026. Ternary complementary ...

In their 2011 paper on the AGT conjecture, Alba, Fateev, Litvinov and Tarnopolsky (AFLT) obtained a closed-form evaluation for Selberg integral over product of two Jack polynomials, thereby unifying well-known Kadell Hua--Kadell integrals. this we use variety symmetric functions function techniques to prove generalisations AFLT integral. These include (i) an $\mathrm{A}_n$ analogue integral, co...

A construction of hexagonal shaped 8-point QAM called H8QAM is shown. H8QAM constellation outperforms the conventional rectangular constellation and 8-PSK. Furthermore, construction of H8QAM Golay sequences having low peak-tomean envelope power ratios (PMEPR) from two QPSK Golay sequences is presented. Various upper bounds on peak envelope powers of these sequences are evaluated.

A decoding algorithm based on Venn diagrams to decode the [23, 12, 71 Golay code is presented. The decoding algorithm is based on the “design” properties of the parity sets of the code. As for other decoding algorithms for the Golay code, decoding can be easily done by hand.

In this paper three different methods and algorithms used to calculate the pairs of Golay sequences of the different length are described. The program for simulating the pairs of the Golay sequences of different length is given. This program (using MatlabTM routines) is based on the basic properties of complementary series and is simple and computationally effective. Experimental results are pr...

Brualdi et al. [Codes with a poset metric, Discrete Math. 147 (1995) 57–72] introduced the concept of poset codes, and gave an example of poset structure which admits the extended binary Golay code to be a 4-error-correcting perfect P-code. In this paper we classify all of the poset structures which admit the extended binary Golay code to be a 4-error-correcting perfect P-code, and show that th...

At present, widely-used radar systems either use very short pulses or linear frequency modulated waveforms, and are based on either monoor bi-static configurations. These systems suffer from having stronger sidelobes, thereby masking weaker returns from subtle changes and making it difficult to detect these changes. To overcome the problem of stronger sidelobes, various coding techniques have b...