## 1 Introduction
This makes it applicable not only to teaching the concepts of error-control codes but also to other disciplines related to algorithmic thinking and binary data processing. Based on this methodology, four interactive software models have been developed: Hamming code utilizing the general algorithm; Hamming code utilizing the matrix algorithm; Cyclic code employing the polynomial algorithm; and Cyclic code based on a linear feedback shift register. Some of these models support both modes of operation--encoding and decoding (Hamming codes), while others support only encoding (Cyclic codes). These models offer an opportunity for a detailed study of the relevant encoding and/or decoding processes, thereby facilitating training in coding theory. Thanks to a unified methodology and design, the developed software models have been successfully integrated into a common virtual laboratory [10], which features various administrative modules for managing the learning process and tracking student progress. This has the potential to enhance teaching effectiveness and enable long-term analysis of learning outcomes and the adaptation of learning strategies. This article focuses solely on the process of designing, implementing, and researching the Hamming code model using the general algorithm, providing a detailed analysis of its functional characteristics and possibilities for interactive learning. In coding theory, Hamming code is one of the basic methods for error detection and correction in digital data transmission. Devised by [PERSON] in 1950, this code was among the very first to allow for effective schemes for the reliable transfer of information with minimal disturbance caused by noise or other forms of errors in communication channels [11]. The applications of Hamming codes are found widely in computer networks, mobile communications, data storage, etc. [12]. The study [13] presents a way to increase the security of QR codes using Hamming codes. A mechanism is proposed for covertly embedding secret messages in QR codes using (8, 4) Hamming codes, where 8 is the total number of bits in the codeword and 4 is the number of information bits. This approach allows for compensation of errors occurring during information embedding through the built-in error correction of QR codes. The results obtained show improvements in the covert message capacity and embedding efficiency, making the method suitable for the secure transmission of sensitive data. The article [14] presents sum-rank Hamming codes, which provide optimal efficiency in single-error correction for multiple matrix-multiplicative channels. The new family of codes is well-suited for applications where the transmission of matrix information needs to be highly reliable. In addition, these codes see application in the construction of locally correctable codes, which is in high demand in contemporary data storage systems. In [15], a method is proposed for hiding confidential information in compressed images using Hamming codes. The described method uses Hamming codes to embed the secret bits while it optimizes the code words and reduces the pixel distortion. Experimental results indicate that this method has satisfactory performance in terms of capacity and image-embedding quality. The application of Hamming codes thus shows their effectiveness in ensuring data integrity in image-based data-hiding techniques. Another study [16] proposes a hybrid steganography method based on least significant bit substitution and Hamming coding. This method increases the capacity for embedding secret messages with the maintenance of high-quality images. Experimental results show that this proposed technique has a higher embedding capacity and better image quality than other techniques. Hamming codes are especially good at single-error correction and double-error detection, which makes them applicable in resource-constrained systems, such as IoT devices and memory modules [17].