human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "on the geometry of balls in the grassmannian and list decoding of lifted gabidulin codes"):
  Abstract: The finite Grassmannian $$\mathcal {G}_{q}(k,n)$$ G q ( k , n ) is defined as the set of all $$k$$ k -dimensional subspaces of the ambient space $$\mathbb {F}_{q}^{n}$$ F q n . Subsets of the finite Grassmannian are called constant dimension codes and have recently found an application in random network coding. In this setting codewords from $$\mathcal {G}_{q}(k,n)$$ G q ( k , n ) are sent through a network channel and, since errors may occur during transmission, the received words can possibly lie in $$\mathcal {G}_{q}(k',n)$$ G q ( k ? , n ) , where $$k'\ne k$$ k ? ? k . In this paper, we study the balls in $$\mathcal {G}_{q}(k,n)$$ G q ( k , n ) with center that is not necessarily in $$\mathcal {G}_{q}(k,n)$$ G q ( k , n ) . We describe the balls with respect to two different metrics, namely the subspace and the injection metric. Moreover, we use two different techniques for describing these balls, one is the Plucker embedding of $$\mathcal {G}_{q}(k,n)$$ G q ( k , n ) , and the second one is a rational parametrization of the matrix representation of the codewords. With these results, we consider the problem of list decoding a certain family of constant dimension codes, called lifted Gabidulin codes. We describe a way of representing these codes by linear equations in either the matrix representation or a subset of the Plucker coordinates. The union of these equations and the linear and bilinear equations which arise from the description of the ball of a given radius provides an explicit description of the list of codewords with distance less than or equal to the given radius from the received word.

Includes members:
  Member "explicit rank metric codes list decodable with optimal redundancy":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "row reduction applied to decoding of rank metric and subspace codes")
  Member "cyclic orbit codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the lattice structure of linear subspace codes")
  Member "bounds on list decoding of rank metric codes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "reliable and secure multishot network coding using linearized reed solomon codes")
  Member "list decoding of lifted gabidulin codes via the plucker embedding":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "list and probabilistic unique decoding of folded subspace codes")
  Member "bounds on list decoding gabidulin codes":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the list decodability of self orthogonal rank metric codes")
  Member "list decoding subspace codes from insertions and deletions":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "analog subspace coding a new approach to coding for non coherent wireless networks")
  Member "decoding of subspace codes a problem of schubert calculus over finite fields":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "problems on q analogs in coding theory")
  Member "list decoding of subspace codes and rank metric codes up to singleton bound":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "list and probabilistic unique decoding of folded subspace codes")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.IT(Information Theory)