The proposed approach to code generation by LLMs, called AlphaCodium, improves the performance of LLMs on challenging code problems through a multi-stage, test-based iterative flow that generates additional data in a pre-processing stage and enriches public tests with AI-generated tests. This approach consistently outperforms previous works, such as AlphaCode, while having a significantly smaller computational budget. The proposed flow is designed to address the complexities of code generation tasks by repeatedly running and fixing generated code against input-output tests, generating additional data through self-reflection and public tests reasoning, and using test anchors to protect against incorrectly fixed code. The approach also employs several design concepts, such as structured output, bullet points analysis, soft decisions with double validation, and postponed decisions, which are found beneficial in solving code generation problems. AlphaCodium outperforms other methods on the CodeContests dataset, including GPT-4, DeepMind fine-tuned models, and CodeChain, while having a lower computational effort, making it more efficient than AlphaCode and AlphaCode2.