One of the most exciting developments of the last two decades in the theory of error-correcting codes has been the discovery of a new class of linear codes called algebraic-geometric (AG) codes. AG codes are known to be more effective than the widely-used Reed- Solomon codes, as they offer greater flexibility in the choice of code parameters. Moreover, it has been proven that there are sequences of AG codes that exceed the Gilbert-Varshamov bound; however, the explicit construction of such AG codes has been an active research topic and is still an open problem. In this project, the following problems are explored: (1) to investigate the explicit construction of sequences of asymptotically good AG codes; and (2) to investigate these constructions to obtain asymptotically good AG codes that exceed the Gilbert-Varshamov bound for codes over GF(q^2), where q is no less than seven.
