Noise reduction is an important part of modern hearing aids and is included in most commercially available devices. Deep learning-based state-of-the-art algorithms, however, either do not consider real-time and frequency resolution constrains or result in poor quality under very noisy conditions.To improve monaural speech enhancement in noisy environments, we propose CLCNet, a framework based on complex valued linear coding. First, we define complex linear coding (CLC) motivated by linear predictive coding (LPC) that is applied in the complex frequency domain. Second, we propose a framework that incorporates complex spectrogram input and coefficient output. Third, we define a parametric normalization for complex valued spectrograms that complies with low-latency and on-line processing.Our CLCNet was evaluated on a mixture of the EUROM database and a real-world noise dataset recorded with hearing aids and compared to traditional real-valued Wiener-Filter gains.