Physical layer security (PLS) draws on the natural randomness of wireless channels to deliver information-theoretic secrecy that does not depend on computational hardness assumptions. In practice, however, existing PLS schemes lose performance when channel conditions worsen and cannot guarantee authenticated secrecy against attackers with stronger antenna arrays. To address both problems, this paper presents a finite-field algebraic coding framework that combines error-correcting codes over GF(2m) with McEliece-type cryptographic encoding, giving reliable transmission and secrecy at once. A randomized parity-check matrix is derived from a Goppa code over GF(28); a secret permutation and a scrambling transformation turn it into the public encoding matrix, while LDPC soft-decision decoding at the intended receiver preserves throughput and leaves the eavesdropper with an NP-hard decoding task. A secrecy-capacity analysis of the Gaussian wiretap channel shows that the scheme still attains a positive secrecy rate when the eavesdropper’s channel is 3 dB better than the legitimate one, which conventional PLS methods cannot do. Tests over OFDM channels with Rayleigh fading give a bit error rate of 10-6 at SNR = 14 dB for the legitimate receiver, an encryption time of 8.4 ms per frame, and a channel capacity utilization of 0.94 bits per channel use, ahead of Reed-Solomon (0.88) and standard McEliece (0.79) under equivalent settings.