The network coding can spread a single original error over the whole network. The simulation shows that the propagated error mostly all the time pollute just 100% of the received packets at the sink if Hamming distance is adopted. If subspace codes are adopted, usually the propagated error will not pollute 100% of the received packets in the sense of subspace distance. However, it also usually pollutes 90% of received packets which is a high error ratio. Even if the rank code and the subspace code are adopted, these existing schemes based on traditional block codes can correct corrupted errors no more than C/2 because of the limitation of the block coding where C is the max flow min cut. It is an agent to find a dense error correction method in random network coding. List decoding of subspace codes can correct $$ \frac{C}{k}\hbox{-} 1 $$ errors where k is the size of information. When $$ \frac{C}{k} $$ is big, many errors in the sense of subspace distance can be corrected. However, the solution of list decoding is not unique. John Wright proposed a dense error correction technique based on L1 minimization, which can recover nearly 100% of the corrupted observations. In our proposal, the original packets are coded with John Wright's coding matrix, and then, the coded message is coded again with subspace codes. In the sink, the decoding procedures about list decoding of subspace codes and John Wright's scheme are performed. At last, the unique solution is achieved even though there are dense propagated errors in random network coding.
Relevance. The relevance of the study is determined by the need for a detailed consideration of the cultural approach in the context of education, in particular, its implementation in educational programmes. Purpose. This research is to identify the differences in the influence of culture on the education systems of China and Kyrgyzstan and to develop recommendations for improving the work of the educational system. Methodology. The following methods were used: system analysis, logical analysis, method of comparison, synthesis, deduction, and method of classification. Results. The study results are presented in the research: attitudes to education in Kyrgyzstan and China are described, the main features of education in Kyrgyzstan and China from the cultural aspect are identified, the main features of Chinese and Kyrgyz pedagogical research in the cultural context are identified, the discourses of the reviewed studies are compared, the main differences and similarities in the cultural aspect of education between Kyrgyzstan and China are presented, the principles underlying the design and development of scientific and pedagogical knowledge are listed and analysed. Conclusions. The research highlights the importance of integrating cultural approaches into modern education, emphasizing the role of cultural heritage in shaping national identity, fostering multicultural competence, and promoting understanding and respect for diverse cultures, ultimately enriching educational experiences and societal development. Keywords: methodological approaches of teaching; national identity; recommendations for improvement; curricula; comparison of approaches; socio-cultural dynamics of society
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