arXiv subjects

Chuangqiang Hu

Publications and source records attributed to Chuangqiang Hu.

22 records · Page 2Linked to original sources

arXiv2016

Weierstrass Semigroups from Kummer Extensions

The Weierstrass semigroups and pure gaps can be helpful in constructing codes with better parameters. In this paper, we investigate explicitly the minimal generating set of the Weierstrass semigroups associated with several totally ramified places over arbitrary Kummer extensions. Applying the techniques provided by Matthews in her previous work, we extend the results of specific Kummer extensions studied in the literature. Some examples are included to illustrate our results.

cs.IT↗

arXiv2016

Multi-point Codes over Kummer Extensions

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.

cs.IT↗

arXiv2015

Explicit Construction of AG Codes from Generalized Hermitian Curves

We present multi-point algebraic geometric codes overstepping the Gilbert-Varshamov bound. The construction is based on the generalized Hermitian curve introduced by A. Bassa, P. Beelen, A. Garcia, and H. Stichtenoth. These codes are described in detail by constrcting a generator matrix. It turns out that these codes have nice properties similar to those of Hermitian codes. It is shown that the duals are also such codes and an explicit formula is given.

cs.IT↗

arXiv2015

Multi-point Codes from Generalized Hermitian Curves

We investigate multi-point algebraic geometric codes defined from curves related to the generalized Hermitian curve introduced by Alp Bassa, Peter Beelen, Arnaldo Garcia, and Henning Stichtenoth. Our main result is to find a basis of the Riemann-Roch space of a series of divisors, which can be used to construct multi-point codes explicitly. These codes turn out to have nice properties similar to those of Hermitian codes, for example, they are easy to describe, to encode and decode. It is shown that the duals are also such codes and an explicit formula is given. In particular, this formula enables one to calculate the parameters of these codes. Finally, we apply our results to obtain linear codes attaining new records on the parameters. A new record-giving $ [234,141,\geqslant 59] $-code over $ \mathbb{F}_{27} $ is presented as one of the examples.

cs.IT↗