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Abstract: The order bound for the minimum distance of algebraic geometry codes wasoriginally defined for the duals of one-point codes and later generalized forarbitrary algebraic geometry codes. Another bound of order type for the minimumdistance of general linear codes, and for codes from order domains inparticular, was given in H. Andersen and O. Geil, Evaluation codes from orderdomain theory, Finite Fields and their Applications 14 2008, pp. 92-123.Here we investigate in detail the application of that bound to one-pointalgebraic geometry codes, obtaining a bound $d^*$ for the minimum distance ofthese codes. We establish a connection between $d^*$ and the order bound andits generalizations. We also study the improved code constructions based on$d^*$. Finally we extend $d^*$ to all generalized Hamming weights.



Author: Olav Geil, Carlos Munuera, Diego Ruano, Fernando Torres

Source: https://arxiv.org/



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