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Designs, Codes and Cryptography

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09-02-2017

Multi-point codes over Kummer extensions

Authors: Chuangqiang Hu, Shudi Yang

Published in: Designs, Codes and Cryptography | Issue 1/2018

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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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Title: Multi-point codes over Kummer extensions
Authors: Chuangqiang Hu
Shudi Yang
Publication date: 09-02-2017
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 1/2018
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0335-7

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