Algebraic manipulation detection codes are a cryptographic primitive that was introduced by Cramer et al. (Eurocrypt 2008). It encompasses several methods that were previously used in cheater detection in secret sharing. Since its introduction, a number of additional applications have been found. This paper contains a detailed exposition of the known results about algebraic manipulation detection codes as well as some new results.
Science China Press
Algebraic Geometric Foundations of Cryptology: The Case of Practical and Unconditionally Secure Computation

Cramer, R.J.F, Fehr, S, & Padró, C. (2013). Algebraic Manipulation Detection Codes. SCIENCE CHINA Mathematics, 56(7), 1349–1358. doi:10.1007/s11425-013-4654-5