Autism spectrum disorder (ASD) is a neurodevelopmental condition that affects the brain's function. Electroencephalography (EEG) is a non-invasive technique that measures the electrical activity of the brain and can reveal its dynamics and information processing. This study explores an eyes-opened resting state quantitative EEG analysis of 49 children with ASD and 39 typically developing (TD or Control) children, using various features of entropy and complexity. Time and frequency domain features were applied for all EEG channels, such as the power spectra, brain rate, sample entropy, permutation entropy, spectral entropy, Tsallis entropy, Rényi entropy, Lempel-Ziv complexity, and Higuchi fractal dimension. The features were compared between the ASD and TD groups and tested for statistical significance. The results showed that the ASD group had a lower brain rate, higher Tsallis entropy and Rényi entropy, and lower Lempel-Ziv complexity than the TD group. The entropy results show impaired neural synchronization, increased randomness, and noise in ASD. The Lempel-Ziv complexity results showed that it is a potential indicator of the existence of focal spikes in the EEG signals of ASD. The brain-rate results show a low level of arousal in ASD. The findings suggest that entropy and complexity measures can be useful tools for characterizing the EEG features of ASD and provide insights into the neurophysiological mechanisms of the disorder.