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 "a tight rate bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures"):
  Abstract: By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local recovery of a set of $t$ erased symbols. There have been several approaches proposed for the handling of multiple erasures. The approach considered here, is one of sequential recovery meaning that the $t$ erased symbols are recovered in succession, each time contacting at most $r$ other symbols for assistance in recovery. Under the constraint that each erased symbol be recoverable by contacting at most $r$ other code symbols, this approach is the most general and hence offers maximum possible code rate. We characterize the maximum possible rate of an LRC with sequential recovery for any $r \geq 3$ and $t$. We do this by first deriving an upper bound on code rate and then going on to construct a {\em binary} code that achieves this optimal rate. The upper bound derived here proves a conjecture made earlier relating to the structure (but not the exact form) of the rate bound. Our approach also permits us to deduce the structure of the parity-check matrix of a rate-optimal LRC with sequential recovery. #R##N#The parity-check matrix in turn, leads to a graphical description of the code. The construction of a binary code having rate achieving the upper bound derived here makes use of this description. Interestingly, it turns out that a subclass of binary codes that are both rate and block-length optimal, correspond to graphs known as Moore graphs that are regular graphs having the smallest number of vertices for a given girth. A connection with Tornado codes is also made in the paper.

Includes members:
  Member "on minimum distance of locally repairable codes":
    also connected through other hyperedges:
      (none)
  Member "binary codes with locality for multiple erasures having short block length":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "new bounds on the field size for maximally recoverable codes instantiating grid like topologies")
  Member "binary codes with locality for four erasures":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "erasure codes for distributed storage tight bounds and matching constructions")
  Member "codes with hierarchical locality":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes")
  Member "binary locally repairable codes sequential repair for multiple erasures":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "erasure codes for distributed storage tight bounds and matching constructions")
  Member "an upper bound on the minimum distance of ldpc codes over gf q":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "erasure codes for distributed storage tight bounds and matching constructions")
  Member "locally repairable codes with functional repair and multiple erasure tolerance":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "erasure codes for distributed storage tight bounds and matching constructions")
  Member "bounds on the parameters of locally recoverable codes":
    also connected through other hyperedges:
      - Hyperedge HE-7 (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)