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Multi-point Codes over Kummer Extensions (1607.05462v1)
Published 19 Jul 2016 in cs.IT and math.IT
Abstract: This paper is concerned with the construction of algebraic geometric codes defined from Kummer extensions. It plays a significant role in the study of such codes to describe bases for the Riemann-Roch spaces associated with totally ramified places. Along this line, we give an explicit characterization of Weierstrass semigroups and pure gaps. Additionally, we determine the floor of a certain type of divisor introduced by Maharaj, Matthews and Pirsic. Finally, we apply these results to find multi-point codes with good parameters. As one of the examples, a presented code with parameters $ [254,228,\geqslant 16] $ over $ \mathbb{F}_{64} $ yields a new record.