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 "functional repair codes a view from projective geometry"):
  Abstract: Storage codes are used to ensure reliable storage of data in distributed systems. Here we consider functional repair codes, where individual storage nodes that fail may be repaired efficiently and the ability to recover original data and to further repair failed nodes is preserved. There are two predominant approaches to repair codes: a coding theoretic approach and a vector space approach. We explore the relationship between the two and frame the later in terms of projective geometry. We find that many of the constructions proposed in the literature can be seen to arise from natural and well-studied geometric objects, and that this perspective gives a framework that provides opportunities for generalisations and new constructions that can lead to greater flexibility in trade-offs between various desirable properties. We also frame the cut-set bound obtained from network coding in terms of projective geometry. We explore the notion of strictly functional repair codes, for which there exist nodes that cannot be replaced exactly. Currently only one known example is given in the literature, due to Hollmann and Poh. We examine this phenomenon from a projective geometry point of view, and discuss how strict functionality can arise. Finally, we consider the issue that the view of a repair code as a collection of sets of vector/projective subspaces is recursive in nature and makes it hard to visualise what a collection of nodes looks like and how one might approach a construction. Here we provide another view of using directed graphs that gives us non-recursive criteria for determining whether a family of collections of subspaces constitutes a function, exact, or strictly functional repair code, which may be of use in searching for new codes with desirable properties.

Includes members:
  Member "cooperative repair constructions of optimal mds codes for all admissible parameters":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "topology aware cooperative data protection in blockchain based decentralized storage networks")
  Member "on the achievability region of regenerating codes for multiple erasures":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "new constructions of cooperative msr codes reducing node size to exp o n")
  Member "a class of msr codes for clustered distributed storage":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "cascade codes for distributed storage systems")
  Member "increasing availability in distributed storage systems via clustering":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "explicit constructions of msr codes for clustered distributed storage the rack aware storage model")
  Member "locality and availability of array codes constructed from subspaces":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes")
  Member "a tight lower bound on the sub packetization level of optimal access msr and mds codes":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "towards practical private information retrieval from mds array codes")
  Member "optimal fractional repetition codes and fractional repetition batch codes":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "bounds on fractional repetition codes using hypergraphs")
  Member "fractional repetition and erasure batch codes":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "load balanced fractional repetition 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.DM(Discrete Mathematics)