The Golay complementary sequences have been studied for more than five decades since Golay first discovered those sequences. However, few studies on the correlation function of transformation form of q-ary complementary sequences. New notions of equivalent transformation on q-ary sequences and equivalent transformation pair of a q-ary sequence and its complex polyphase form are put forward. A t...

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...

The perfect Golay codes lifted over the finite rings Z2m and Z3m, or over their infinite counterparts, namely the 2-adic and 3-adic rings, are considered, and their algebraic decoding is obtained as a non-trivial extension of the algebraic decoding of the perfect Golay codes. Mathematics Subject Classification: 94B15, 94B35, 11D88, 14G50

This study investigates a new composing method of double transmission of short coded sequences based on well-known Golay complementary codes, which allow to obtain the higher signal-to-noise ratio (SNR) and increase penetration depth. The proposed method can potentially find application in small parts ultrasonography and play important role in examination of superficial structures, e.g. in derm...