We study error detection and correction in a computationally bounded world, where errors are introduced by an arbitrary polynomial-time adversarial channel. Our focus is on seeded codes, where the encoding and decoding procedures can share a public random seed, but are otherwise deterministic. We can ask for either selective or adaptive security, depending on whether the adversary can choose the message being encoded before or after seeing the seed. For large alphabets, a recent construction achieves essentially optimal rate versus error tolerance trade-offs under minimal assumptions, surpassing information-theoretic limits. However, for the binary alphabet, the only prior improvement over information theoretic codes relies on non-standard assumptions justified via the random oracle model. We show the following: