## 1 Introduction  
In modern education, there is a growing need for interactive learning tools [1, 2, 3, 4] to support the learning of complex theoretical concepts. Traditional teaching methods often make it difficult for students to understand abstract mathematical and technical courses, which necessitates the development of innovative learning technologies. Interactive software models offer visualizations, simulations, and practical exercises that facilitate understanding and apply concepts in real-world scenarios. By being adaptable and personalized to the needs of learners, these tools could increase engagement, motivation, and learning outcomes. Educational software has evolved from static computer-based learning systems to interactive, adaptive, and gamified environments in recent decades. Early educational software systems focused primarily on presenting static learning materials, such as text, images, and pre-recorded video lessons. These platforms are primarily based on a linear teaching structure, in which students follow a predetermined learning \"path\". While this model is effective for certain disciplines, it does not offer dynamic adaptation to individual learner needs [5]. One of the main disadvantages of non-interactive learning platforms is the passive participation of learners. Some studies claim that active engagement and immediate feedback when solving problems and simulations lead to better perception of information and, respectively, to better results [5; 6; 7]. Therefore, the focus of modern educational platforms is on the inclusion of interactive simulations, problem-solving exercises, and adaptive learning techniques to ensure the individual needs of students [8]. In areas requiring a deep understanding of abstract mathematical concepts, such as coding theory, these educational approaches would be extremely valuable. Error-control codes, which play a key role in ensuring the reliability of communication systems, are extremely important for understanding and applying basic principles in information technology. The introduction of interactive software learning models could provide students with the opportunity to master these concepts in a way that is both visual and practical. Research on interactive learning tools shows that such technologies can improve student understanding and retention, especially when combined with gamification elements [9]. Gamified systems can include mechanisms such as points, levels, achievements, and challenges that would motivate students to complete assignments and progress in their learning [9]. By integrating problem-solving exercises, automated feedback, and adaptive difficulty levels, educational software can bridge the gap between theoretical information and practical application. This article proposes a general methodology for designing and creating an interactive software model intended to support the learning of various codes from coding theory. The methodology provides a systematic and unified approach to the development of educational environments, focusing on the algorithmic and programmatic aspects of modeling, along with key principles of interactive learning. Unlike traditional static learning materials and passive simulations (simple animations with limited or no interaction), the proposed model integrates modern interactive technologies, which include:  
* Real-time feedback--students receive automated guidance and analysis of their errors during task completion. * Gamification through a point system and individual tasks--engaging students by dynamically assigning exercises with progressive difficulty. * Process visualization--presenting the computational steps in encoding and/or decoding, which supports understanding abstract concepts. The proposed framework builds on existing educational solutions by providing a standardized approach for developing interactive software environments. It combines theoretical training with practical experiments, allowing for both teaching and research on the effectiveness of interactive methods.