This paper proposes the design of discrete frequency-coded (DFC) waveforms that have an ambiguity function with no sidelobes around the central mainlobe. Different approaches for enhancing the sidelobe free area in delay-Doppler plane are explained. Sidelobe pushing property of Costas arrays is discussed. LC codes are suggested for achieving higher sidelobe free region with smaller sequence lengths. The results presented here show that by using LC codes, larger clear area around the mainlobe can be obtained with smaller code length compared to Costas codes.