In a hybrid codec apparatus for data broadcasting, an encoder divides a source file into N sections, generates N principal encoded data after coding on a first finite field and k additional encoded data after coding on a second finite field, then transmits a group of coefficient encoded data and the N+k encoded data to a decoder. The decoder merges the group of coefficient encoded data and the N+k encoded data, and decodes the N principal encoded data on the first finite field. When the decoder fails to decode the N principal encoded data, the decoder uses the k additional encoded data to assist the data decoding on the second finite field. After the decoding, a recovered source file is produced.