In this study, a class of Generalized Low-Density Parity-Check (GLDPC) codes is designed for data transmission over a Partial-Band Jamming (PBJ) environment. The GLDPC codes are constructed by replacing parity-check code constraints with those of nonsystematic Bose-Chaudhuri-Hocquenghem (BCH), referred to as Low-Density Parity-Check (LDPC)-BCH codes. The rate of an LDPC-BCH code is adjusted by selecting the transmission length of the nonsystematic BCH code, and a low-complexity decoding algorithm based on message-passing is presented that employs A Posteriori Probability (APP) fast BCH transform for decoding the BCH check nodes at each decoding iteration. Simulation results show that the LDPC-BCH codes with a code rate of 1/8.5 have a bit error rate performance of 1 $\mathrm{\times }$10 ${}^{\mathrm{-}6}$ at signal-noise-ratios of $\mathrm{-}$6.97 dB, $\mathrm{-}$4.63 dB, and 2.48 dB when the fractions of the band jammed are 30%, 50%, and 70%, respectively.