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 "how long can optimal locally repairable codes be"):
  Abstract: A locally repairable code (LRC) with locality $r$ allows for the recovery of any erased codeword symbol using only $r$ other codeword symbols. A Singleton-type bound dictates the best possible trade-off between the dimension and distance of LRCs --- an LRC attaining this trade-off is deemed \emph{optimal}. Such optimal LRCs have been constructed over alphabets growing linearly in the block length. Unlike the classical Singleton bound, however, it was not known if such a linear growth in the alphabet size is necessary, or for that matter even if the alphabet needs to grow at all with the block length. Indeed, for small code distances $3,4$, arbitrarily long optimal LRCs were known over fixed alphabets. #R##N#Here, we prove that for distances $d \ge 5$, the code length $n$ of an optimal LRC over an alphabet of size $q$ must be at most roughly $O(d q^3)$. For the case $d=5$, our upper bound is $O(q^2)$. We complement these bounds by showing the existence of optimal LRCs of length $\Omega_{d,r}(q^{1+1/\lfloor(d-3)/2\rfloor})$ when $d \le r+2$. These bounds match when $d=5$, thus pinning down $n=\Theta(q^2)$ as the asymptotically largest length of an optimal LRC for this case.

Includes members:
  Member "optimal lrc codes for all lenghts n q":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "erasure codes for distributed storage tight bounds and matching constructions")
  Member "optimal locally repairable codes of distance 3 and 4 via cyclic codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "constructive asymptotic bounds of locally repairable codes via function fields")
  Member "optimal locally repairable codes via elliptic curves":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes")
  Member "a family of optimal locally recoverable codes":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a locality based approach for coded computation")
  Member "xoring elephants novel erasure codes for big data":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes")
  Member "on the locality of codeword symbols in non linear codes":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "new bounds on the field size for maximally recoverable codes instantiating grid like topologies")
  Member "an upper bound on the size of locally recoverable codes":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "the complete hierarchical locality of the punctured simplex code")
  Member "optimal locally repairable codes and connections to matroid theory":
    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)