Designs, Codes and Cryptography
Designs, Codes and Cryptography
Algebraic geometry codes from polyhedral divisors
Journal of Symbolic Computation
On the parameters of r-dimensional toric codes
Finite Fields and Their Applications
Error-correcting codes on projective bundles
Finite Fields and Their Applications
Toric complete intersection codes
Journal of Symbolic Computation
On the evaluation of multivariate polynomials over finite fields
Journal of Symbolic Computation
Evaluation codes from smooth quadric surfaces and twisted Segre varieties
Designs, Codes and Cryptography
A new family of locally correctable codes based on degree-lifted algebraic geometry codes
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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In this paper we use intersection theory to develop methods for obtaining lower bounds on the parameters of algebraic geometric error-correcting codes constructed from varieties of arbitrary dimension. The methods are sufficiently general to encompass many of the codes previously constructed from higher-dimensional varieties, as well as those coming from curves. And still, the bounds obtained are usually as good as the ones previously known (at least of the same order of magnitude with respect to the size of the ground field). Several examples coming from Deligne-Lusztig varieties, complete intersections of Hermitian hyper-surfaces, and from ruled surfaces (or more generally, projective bundles over a curve) are given.