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...

This study concerns the development and investigation of a new composing method of short coded sequences and their transmission based on well-known Golay complementary codes and applied compression technique allowing to increase the signal-to-noise ratio (SNR) and penetration. This new method can potentially play important role in examination of superficial structures, e.g. dermatology, ophthal...

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...

Complementary sequences were introduced by Marcel Golay [1] in the context of infrared spectrometry. A complementary pair of sequences (CS pair) satis£es the useful property that their out-of-phase aperiodic autocorrelation coef£cients sum to zero [1, 2]. Let a = (a0, a1, . . . , aN−1) be a sequence of length N such that ai ∈ {+1,−1} (we say that a is bi-polar). De£ne the Aperiodic Auto-Correla...

Borwein and Mossinghoff investigated the Rudin-Shapirolike polynomials, which are infinite families of Littlewood polynomials, that is, polynomials whose coefficients are all in {−1, 1}. Each family of Rudin-Shapiro-like polynomials is obtained from a starting polynomial (which we call the seed) by a recursive construction. These polynomials can be regarded as binary sequences. Borwein and Moss...

The Pursley-Sarwate criterion of a pair of finite complex-valued sequences measures the collective smallness of the aperiodic autocorrelations and the aperiodic crosscorrelations of the two sequences. It is known that this quantity is always at least 1 with equality if and only if the sequence pair is a Golay pair. We exhibit pairs of complex-valued sequences whose entries have unit magnitude f...

power, envelope, OFDM, Reed-Muller, code, Golay, complementary, sequence, pair, set Practical communications engineering is continuously producing problems in interest to the coding theory community. A recent example is the power-control problem in Orthogonal Frequency Division Multiplexing (OFDM). We report recent work which gives a mathematical framework for generating solutions to this notor...

We argue that a Golay complementary sequence is naturally viewed as a projection of a multidimensional Golay array. We present a three-stage process for constructing and enumerating Golay array and sequence pairs: 1. construct suitable Golay array pairs from lower-dimensional Golay array pairs; 2. apply transformations to these Golay array pairs to generate a larger set of Golay array pairs; an...

In this paper, we introduce the definitions of Eulerian pair and Hermite-Biehler pair. We also characterize a duality relation between recurrences recurrence systems. This generalizes unifies decompositions several enumerative polynomials, including up-down run polynomials for symmetric groups, alternating hyperoctahedral flag descent groups ascent-plateau Stirling permutations. derive some pro...