## 2 Materials and Methods
#### 2.2.2 Analysis of the Theoretical Foundations of the Hamming Code by the General Method
\[C_{1} =>\ C_{1}\oplus S_{1}\oplus S_{2}\oplus S_{4}\oplus S_{5}\oplus S_{7} \oplus S_{9}=1\oplus 1\oplus 1\oplus 0\oplus 0\oplus 0\oplus 1=0 \tag{20}\]  
\[C_{2} =>\ C_{2}\oplus S_{1}\oplus S_{3}\oplus S_{4}\oplus S_{6}\oplus S_{7}=1 \oplus 1\oplus 0\oplus 0\oplus 1\oplus 0=1 \tag{21}\]  
\[C_{3} =>\ C_{3}\oplus S_{2}\oplus S_{3}\oplus S_{4}\oplus S_{8}\oplus S_{9}=0 \oplus 1\oplus 0\oplus 0\oplus 1\oplus 1=1 \tag{22}\]Error syndrome: \(C_{4}C_{3}C_{2}C_{1}=>0\;1\;1\;0=>\) error indication Error position: \((0\;1\;1\;0)_{2}=(6)_{10}\)  
After converting the syndrome into decimal format, it can be seen that the wrong bit is in position \(N\;6\), which is proof of the correctness of the solution because an artificial error was made exactly in the sixth position at the beginning of the problem. To obtain the correct code combination, the value of the bit at this position should be corrected (inverted). \[\left[X\right]\;\begin{array}{|  
Encoding mode (Figure 6a)  
Defining the code parameters. Based on the condition of the task, the parameters \(m\), \(l_{0}\), \(k\), and \(n\) are determined. Step (1) Determining the type of bits of the code combination. In this step, it is necessary to determine (mark) the bits of the code combination of what type they are (control or information). Step (2) Write the information bits in the code combination. In this step, the information bits are written to their corresponding positions in the code combination. Step (3) Defining the control bits. This step is performed in several stages. Step (4.1) Select the control bit to calculate. The selection can be made from any control bit except the control bit \(C_{0}\) (in the extended code), which must be selected last. Step (4.2) Formulation of the control bit equation. The check-bit equations are formed following the general rule presented in point 2.2.2. Step (4.3) Calculating the check bit. The operations in this step consist of substituting the binary values of the information bits involved into the equation being composed and performing a modulo 2 addition. Steps 4.1 to 4.3 are performed for each control bit. Decoding Mode--Figure 6b  
Step (1) Corresponds to step (1) of the encoding mode. Step (2) Matches step (2) of the encoding mode. Step (3) Checking control bits. This action is performed in several stages:  
Step (3.1) Select the control bit to check. The selection can be made from any control bit. Figure 6: Algorithm of solving Hamming code problems by the general method. (**a**) encoding. (**b**) decoding. Step (3.2) Formulation of the control ratio equation. They are composed similarly to the equations of the control bits. Step (3.3) Calculation of the ratio. The values from the code combination are substituted into the control ratio, and addition modulo 2 is performed. Steps 3.1 through 3.3 are performed for each control bit. Step (4) Analysis of the result. The error syndrome is written in binary form and then converted to decimal format. Depending on the syndrome, the status of the error is determined (\"No error\", \"Single error\", and \"Double error\"). If there is a single error in the code combination, its position is determined and corrected by inverting the bit value of that position. Step (5) Determining the decoded binary information. From the resulting code combination, only the values of the information bits are written, in case the error status in Step 4 is \"No error\" or \"Single error\" (after correcting the erroneous bit); otherwise, the code is unable to decode the code combination. 2.4 Formulation of the Requirements for the Interactive Hamming Code Research Model--The General Method  
* General requirements for the interactive software models  
Interactive programming models for solving tasks for the study of channel codes should have similar characteristics and principles of operation, which means that a unified interface should be designed so that after familiarizing with one model, the user can easily and quickly navigate and adapt to the others.