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09.02.2017 | Ausgabe 1/2018

Designs, Codes and Cryptography 1/2018

Multi-point codes over Kummer extensions

Zeitschrift:
Designs, Codes and Cryptography > Ausgabe 1/2018
Autoren:
Chuangqiang Hu, Shudi Yang
Wichtige Hinweise
Communicated by G. Korchmaros.

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 present 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 excellent parameters. As one of the examples, a presented code with parameters \([254,228,\geqslant 16]\) over \( {\mathbb {F}}_{64} \) yields a new record.

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