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 "bounds and constructions of locally repairable codes parity check matrix approach"):
  Abstract: A code symbol of a linear code is said to have locality r if this symbol could be recovered by at most r other code symbols. An (n,k,r) locally repairable code (LRC) with all symbol locality is a linear code with length n, dimension k, and locality r for all symbols. Recently, there are lots of studies on the bounds and constructions of LRCs, most of which are essentially based on the generator matrix of the linear code. Up to now, the most important bounds of minimum distance for LRCs might be the well-known Singleton-like bound and the Cadambe-Mazumdar bound concerning the field size. #R##N#In this paper, we study the bounds and constructions of LRCs from views of parity-check matrices. Firstly, we set up a new characterization of the parity-check matrix for an LRC. Then, the proposed parity-check matrix is employed to analyze the minimum distance. We give an alternative simple proof of the well-known Singleton-like bound for LRCs with all symbol locality, and then easily generalize it to a more general bound, which essentially coincides with the Cadambe-Mazumdar bound and includes the Singleton-like bound as a specific case. Based on the proposed characterization of parity-check matrices, necessary conditions of meeting the Singleton-like bound are obtained, which naturally lead to a construction framework of good LRCs. Finally, two classes of optimal LRCs based on linearized polynomial theories and Vandermonde matrices are obtained under the construction framework.

Includes members:
  Member "constructions of optimal cyclic r delta locally repairable codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes")
  Member "constructions and properties of linear locally repairable codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "alphabet dependent bounds for linear locally repairable codes based on residual codes")
  Member "optimal linear and cyclic locally repairable codes over small fields":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the complete hierarchical locality of the punctured simplex code")
  Member "optimal binary locally repairable codes via anticodes":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "new bounds on the field size for maximally recoverable codes instantiating grid like topologies")
  Member "cyclic lrc codes and their subfield subcodes":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "locally recoverable j affine variety codes")
  Member "achieving arbitrary locality and availability in binary codes":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "pir codes with short block length")
  Member "binary linear locally repairable codes":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "new bounds on the field size for maximally recoverable codes instantiating grid like topologies")
  Member "bounds on the parameters of locally recoverable codes":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "on optimal locally repairable codes and generalized sector disk 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)