Goppa codes

Goppa codes are a type of error-correcting codes used in digital communications to detect and fix errors that occur during data transmission. They are constructed using mathematical objects called Goppa polynomials and finite fields, allowing for efficient error correction. These codes are known for their strong error-correcting capabilities and are foundational in cryptography and secure communication systems, including the McEliece cryptosystem. By adding redundancy based on algebraic structures, Goppa codes help ensure received data matches the original message despite noise or interference during transmission.