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pro vyhledávání: '"Hu, Chuangqiang"'
Let $ (X,0) $ denote an isolated singularity defined by a weighted homogeneous polynomial $ f $. Let $ \mathcal{O}$ be the local algebra of all holomorphic function germs at the origin with the maximal ideal $m $. We study the $k$-th Tjurina algebra,
Externí odkaz:
http://arxiv.org/abs/2409.09384
Autor:
Hu, Chuangqiang, Huang, Xiao-Min
The primary objective of this paper is to derive explicit formulas for rank one and rank two Drinfeld modules over a specific domain denoted by A. This domain corresponds to the projective line associated with an infinite place of degree two. To achi
Externí odkaz:
http://arxiv.org/abs/2312.16919
We introduce normalized Drinfeld modular curves that parameterize rank $m$ Drinfeld modules compatible with a $T$-torsion structure arising from a given conjugacy class of nilpotent upper-triangular $n\times n$ matrices with rank $\geqslant n-m$ over
Externí odkaz:
http://arxiv.org/abs/2309.00432
In 2000, based on his procedure for constructing explicit towers of modular curves, Elkies deduced explicit equations of rank-2 Drinfeld modular curves which coincide with the asymptotically optimal towers of curves constructed by Garcia and Stichten
Externí odkaz:
http://arxiv.org/abs/1912.02668
Autor:
Yang, Shudi, Hu, Chuangqiang
For applications in algebraic geometric codes, an explicit description of bases of Riemann-Roch spaces of divisors on function fields over finite fields is needed. We investigate the third function field $ F^{(3)} $ in a tower of Artin-Schreier exten
Externí odkaz:
http://arxiv.org/abs/1911.04269
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In 1997, Shor and Laflamme defined the weight enumerators for quantum error-correcting codes and derived a MacWilliams identity. We extend their work by introducing our double weight enumerators and complete weight enumerators. The MacWilliams identi
Externí odkaz:
http://arxiv.org/abs/1810.11969
Autor:
Hu, Chuangqiang, Yang, Shudi
This paper is concerned with the construction of algebraic geometric codes defined from GGS curves. It is of significant use to describe bases for the Riemann-Roch spaces associated with totally ramified places, which enables us to study multi-point
Externí odkaz:
http://arxiv.org/abs/1706.00313
Autor:
Yang, Shudi, Hu, Chuangqiang
In this paper, by employing the results over Kummer extensions, we give an arithmetic characterization of pure gaps at many totally ramified places over the quotients of Hermitian curves, including the well-studied Hermitian curves as special cases.
Externí odkaz:
http://arxiv.org/abs/1705.05213
Autor:
Yang, Shudi, Hu, Chuangqiang
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 ov
Externí odkaz:
http://arxiv.org/abs/1607.05887