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Algebra has played an important role since the early age of coding theory, where finite fields and later on algebraic curves, have been used to design error-correcting codes. Recently, the emergence of wireless communication has attracted the attention of coding theoretists. New coding problems have arisen, which require new tools. In this talk, I will present several wireless coding problems, and show that algebraic techniques coming from algebraic number theory or the theory of central simple algebras are suitable tools to develop efficient solutions.