Linear codes

Linear codes are a method used in digital communication to detect and correct errors that occur during data transmission. They work by adding extra, carefully structured bits to the original message, forming a codeword. These added bits make the codeword belong to a specific mathematical space called a linear space, which allows efficient checking for errors and fixing them when data is received. Essentially, linear codes help ensure that messages arrive accurately even in noisy or imperfect communication channels by leveraging the properties of linear algebra.