Background: Feedback as one of the most influential factors for learning has been subject to a great body of research. It plays a key role in the development of educational technology systems and is traditionally rooted in deterministic feedback defined by experts and their experience. However, with the rise of generative AI and especially large language models (LLMs), we expect feedback as part of learning systems to transform, especially for the context of programming. In the past, it was challenging to automate feedback for learners of programming. LLMs may create new possibilities to provide richer, and more individual feedback than ever before. Objectives: This article aims to generate specific types of feedback for introductory programming tasks using LLMs. We revisit existing feedback taxonomies to capture the specifics of the generated feedback, such as randomness, uncertainty and degrees of variation. Methods: We iteratively designed prompts for the generation of specific feedback types (as part of existing feedback taxonomies) in response to authentic student programs. We then evaluated the generated output and determined to what extent it reflected certain feedback types. Results and Conclusion: This study provides a better understanding of different feedback dimensions and characteristics. The results have implications for future feedback research with regard to, for example, feedback effects and learners' informational needs. It further provides a basis for the development of new tools and learning systems for novice programmers including feedback generated by AI.