This paper presents a construction of regular low-density parity-check (LDPC) codes based on the incidence matrices of oval designs. The codes from this class have good minimum distances and Tanner graphs free of 4-cycles. Like the codes obtained from finite geometries, the oval codes have parity-check matrices with a large proportion of linearly dependent rows. Further, by exploiting the resolvability of oval designs, we are able to produce a wide range of code rates and lengths while maintaining code regularity.