Formalization of Reed-Solomon codes and progress report on formalization of LDPC codes

Error-correcting codes make possible reliable communication over noisy channels. One way to guarantee the correct implementation of error-correcting codes is to use formal verification. This requires in particular the formalization of the mathematical theory of error-correcting codes. This has been made possible by recent advances in the formalization of mathematics using proof-assistants. In this paper, we discuss formalization of linear error-correcting codes: we introduce a formalization of cyclic codes and Euclidean decoding that we apply to Reed-Solomon codes, and we discuss the advanced topic of LDPC codes.