Linear codes are a type of error-correcting code used in digital communication to ensure that data is transmitted accurately. They work by taking a set of input data and transforming it into a longer codeword through a linear combination of the input bits. This process helps detect and correct errors that may occur during transmission, making communication more reliable. One of the key features of linear codes is their use of vector spaces in coding theory. Each codeword can be represented as a point in a vector space, allowing for efficient encoding and decoding processes. Popular examples of linear codes include Hamming codes and Reed-Solomon codes, which are widely used in various applications, from data storage to telecommunications.