## 2 Methodology
### Code Generation and Compression  
Generally, coded excitation is an ultrasound technique that has been used for ultrasound imaging systems in medical applications. The improvement of SNR is related to the sequence length. The features of the sequence of the conventional Golay codes and barker codes is infinite and finite, respectively, [25]. Theoretically, the longer code excitation sequence offers better performance of the SNR but a higher axial resolution depends on a shorter input signal wavelength. Therefore, the selection of the code excitation sequence length needs to be considered for accuracy and efficiency of defect detection under different applications. Currently, the combined code excitation method is only applied to ultrasound imaging applications, and it has few selections for the combined code sequences available [5]. However, there is no existing literature and usage on the excitation of guided waves for long-range distance detection at low-frequencies. In this paper, this developed technique is successfully achieved to use on the guided wave generation and propagation for pipeline inspection theoretically and experimentally. Golay codes and Barker codes are called their specific lengths and sequences. The BCG is convoluted by Golay code and Barker code, which may result in further improvement in signal intensity and adaptability for code length compared to the convention of Golay code pair or Barker code. The combined codes have an equivalent sidelobe intensity of the Baker code used. The main lobe intensity of the combined codes is similar to the sum of the main lobe intensity of Barker code and Golay code pair. Therefore, the developed BCG code sequence covers the advantages of the two codes including a high main lobe intensity of Barker code and Golay code pair without side lobes. To excite a continuous signal, the BCG code needs to be modulated by a carrier wave (a bit like a sine wave). Transmit beamformer and electrical device are to generate and transmit the BCG coded signal. The electrical device will receive the echo signals from medium. Figure 2 shows the workflow how to generate the BCG codes and compress the echo. Firstly, the BCG code sequences are made by the convolution of the designed length of Barker code and the designed length of Golay code pair. Then, the BCG code sequences are modulated and transmitted to the medium to obtain a pair of echoes. Later, the echoes need to be compressed. There are two steps to compress the echoes. The primary step is to compress a pair of echo signals using the specific Golay code pair matched filter. The second step is to compress the signals processed in the previous step by the fitted Barker code matched filter. The compression result is the superposition of the processed echo signal pairs. Figure 1: Group velocity dispersion curves for a 8-inch, schedule 40 steel pipe. A BCG code pair, \(BCG_{a}\) and \(BCG_{b}\), are built using the convolution of Golay sequence and Barker sequence and then modulated by a base pulse, as shown by the following equations. \[BCG_{a}(n) = G_{a}(n)*B(n)*S(n) \tag{1}\] \[BCG_{b}(n) = G_{b}(n)*B(n)*S(n) \tag{2}\]  
where \(B(n)\) is a known Barker code sequence and \(G_{a}(n)\), \(G_{b}(n)\) are the Golay code pairs. Defined the \(BCG_{a}(n)\) and \(BCG_{b}(n)\) as modulated BCG code signal. \(S(n)\) is a carrier sine wave. There is an example of transmitted b3g4 (Baker (\(n=3\)) and Golay (\(n=4\))) code pair in Figure 3. It shows that the b3g4 code pair sequence is generated by the 3-bit Barker code and the 4-bit Golay code pair. To obtain a pair of transmission signals, the obtained complementary pair will be modulated by the sine wave. To prove the feasibility of BCG code, the theoretical analysis based on synthetic input/output signals has been done. There are 15 different types of BCG codes to use for analysis. Three different types of pulses have been used: a simple pulse, 7-bit Barker code and 4-bit Golay code pair. The SNR gain is given by Equation (3).