In this paper, we propose a framework to allocate code rates of component codes in a Plotkin-type unequal error protection (UEP) code. We derive an equivalent noise variance for each component code using structure of the Plotkin construction and Gaussian assumption. Comparing the equivalent noise variance and Shannon limit, we can find a combination of the code rates for the component codes. We investigate three types of code rate combinations and analyse their UEP performance. We also estimate a performance crossing signal to noise ratio (SNR) of the Plotkin-type UEP code. It indicates that which code has better performance for a given SNR. We confirm that the proposed framework is appropriate to obtain a desired UEP capability.

Gopalan, Klivans, and Zuckerman proposed a list-decoding algorithm for Reed-Muller codes. Their algorithm works up to a given list-decoding radius. Dumer, Kabatiansky, and Tavernier improved the complexity of the algorithm for binary Reed-Muller codes by using the well-known Plotkin construction. In this study, we propose a list-decoding algorithm for non-binary Reed-Muller codes as a generalization of Dumer et al.'s algorithm. Our algorithm is based on a generalized Plotkin construction, and is more suitable for parallel computation than the algorithm of Gopalan et al. Since the list-decoding algorithms of Gopalan et al., Dumer et al., and ours can be applied to more general codes than Reed-Muller codes, we give a condition for codes under which these list-decoding algorithms works.