Radar waveform design is a long standing area of interest and research in the radar community. Recently, radar waveform design has been paired with Sudoku, a logic puzzle that has been popular worldwide since the 1980s. The combination of the two has spurred a new area of radar research: Sudoku based radar waveform design. In this paper, we compare Sudoku based Multicarrier Phase-Coded (MCPC) signals to both Costas codes and random codes for different transmitted pulse structures. We provide computational results in the form of statistical analysis for the autocorrelation function and analytical ambiguity function analysis, as well as measurements of the Peak Side Lobe Level (PSL) of their Autocorrelation Function (ACF). We then assess the closeness of the resulting ambiguity function to the ideal thumbtack response.