human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "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.

Connected through hyperedge HE-1 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes"):
  with members:
    - "array codes with local properties"
    - "universal and dynamic locally repairable codes with maximal recoverability via sum rank codes"
    - "explicit construction of optimal locally recoverable codes of distance 5 and 6 via binary constant weight codes"
    - "on optimal locally repairable codes with super linear length"
    - "explicit optimal length locally repairable codes of distance 5"
    - "locality and availability of array codes constructed from subspaces"
    - "optimal locally repairable codes via elliptic curves"
    - "bounds and constructions of codes with multiple localities"

Connected through hyperedge HE-2 (induced by source paper "locally recoverable j affine variety codes"):
  with members:
    - "combinatorial alphabet dependent bounds for locally recoverable codes"
    - "new binary and ternary lcd codes"
    - "classical and quantum evaluation codes at the trace roots"
    - "on the distance of stabilizer quantum codes from j affine variety codes"
    - "constructions of optimal cyclic r delta locally repairable codes"
    - "stabilizer quantum codes from j affine variety codes and a new steane like enlargement"
    - "cooperative local repair in distributed storage"
    - "cyclic lrc codes and their subfield subcodes"

Connected through hyperedge HE-3 (induced by source paper "constructive asymptotic bounds of locally repairable codes via function fields"):
  with members:
    - "explicit construction of optimal locally recoverable codes of distance 5 and 6 via binary constant weight codes"
    - "construction of optimal locally recoverable codes and connection with hypergraph"
    - "optimal locally repairable codes of distance 3 and 4 via cyclic codes"
    - "construction of asymptotically good locally repairable codes via automorphism groups of function fields"
    - "construction of optimal locally repairable codes via automorphism groups of rational function fields"
    - "optimal locally repairable codes via elliptic curves"
    - "bounds on the parameters of locally recoverable codes"
    - "locally recoverable codes on algebraic curves"

Connected through hyperedge HE-4 (induced by source paper "locally recoverable codes on surfaces"):
  with members:
    - "locally recoverable codes from algebraic curves with separated variables"
    - "optimal locally repairable codes via elliptic curves"
    - "locally recoverable codes on algebraic curves"
    - "a family of optimal locally recoverable codes"
    - "locally repairable codes"
    - "on the locality of codeword symbols"

Connected through hyperedge HE-5 (induced by source paper "universal and dynamic locally repairable codes with maximal recoverability via sum rank codes"):
  with members:
    - "maximally recoverable codes with hierarchical locality"
    - "reliable and secure multishot network coding using linearized reed solomon codes"
    - "extended integrated interleaved codes over any field with applications to locally recoverable codes"
    - "random construction of partial mds codes"
    - "constructions of maximally recoverable local reconstruction codes via function fields"
    - "locally repairable codes with unequal local erasure correction"
    - "optimal locally repairable codes of distance 3 and 4 via cyclic codes"
    - "skew and linearized reed solomon codes and maximum sum rank distance codes over any division ring"

Connected through hyperedge HE-6 (induced by source paper "on optimal locally repairable codes with super linear length"):
  with members:
    - "combinatorial alphabet dependent bounds for locally recoverable codes"
    - "explicit construction of optimal locally recoverable codes of distance 5 and 6 via binary constant weight codes"
    - "optimal lrc codes for all lenghts n q"
    - "optimal locally repairable codes of distance 3 and 4 via cyclic codes"
    - "explicit optimal length locally repairable codes of distance 5"
    - "irregular recovery and unequal locality for locally recoverable codes with availability"
    - "locality and availability of array codes constructed from subspaces"
    - "optimal locally repairable systematic codes based on packings"

Connected through hyperedge HE-7 (induced by source paper "explicit construction of optimal locally recoverable codes of distance 5 and 6 via binary constant weight codes"):
  with members:
    - "optimal lrc codes for all lenghts n q"
    - "construction of optimal locally recoverable codes and connection with hypergraph"
    - "optimal locally repairable codes of distance 3 and 4 via cyclic codes"
    - "construction of optimal locally repairable codes via automorphism groups of rational function fields"
    - "locally recoverable codes from algebraic curves and surfaces"
    - "optimal locally repairable codes via elliptic curves"
    - "cyclic lrc codes binary lrc codes and upper bounds on the distance of cyclic codes"
    - "locally recoverable codes on algebraic curves"

Connected through hyperedge HE-8 (induced by source paper "explicit optimal length locally repairable codes of distance 5"):
  with members:
    - "explicit construction of optimal locally recoverable codes of distance 5 and 6 via binary constant weight codes"
    - "affine cartesian codes with complementary duals"
    - "optimal locally repairable codes of distance 3 and 4 via cyclic codes"
    - "construction of optimal locally repairable codes via automorphism groups of rational function fields"
    - "locally recoverable codes from algebraic curves and surfaces"
    - "optimal locally repairable codes via elliptic curves"
    - "a family of optimal locally recoverable codes"
    - "optimal locally repairable codes via rank metric codes"

Question: Please tell me which class the center node 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)