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 "on the weight hierarchy of locally repairable codes"):
  Abstract: An $(n,k,r)$ \emph{locally repairable code} (LRC) is an $[n,k,d]$ linear code where every code symbol can be repaired from at most $r$ other code symbols. An LRC is said to be optimal if the minimum distance attains the Singleton-like bound $d \le n-k-\lceil k/r \rceil +2$. The \emph{generalized Hamming weights} (GHWs) of linear codes are fundamental parameters which have many useful applications. Generally it is difficult to determine the GHWs of linear codes. In this paper, we study the GHWs of LRCs. Firstly, we obtain a generalized Singleton-like bound on the $i$-th $(1\le i \le k)$ GHWs of general $(n,k,r)$ LRCs. Then, it is shown that for an optimal $(n,k,r)$ LRC with $r \mid k$, its weight hierarchy can be completely determined, and the $i$-th GHW of an optimal $(n,k,r)$ LRC with $r \mid k$ attains the proposed generalized Singleton-like bound for all $1\le i \le k$. For an optimal $(n,k,r)$ LRC with $r \nmid k$, we give lower bounds on the GHWs of the LRC and its dual code. Finally, two general bounds on linear codes in terms of the GHWs are presented. Moreover, it is also shown that some previous results on the bounds of minimum distances of linear codes can also be explained or refined in terms of the GHWs.

Includes members:
  Member "on optimal ternary locally repairable codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "erasure codes for distributed storage tight bounds and matching constructions")
  Member "bounds and constructions of locally repairable codes parity check matrix approach":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "bounds and constructions for linear locally repairable codes over binary fields")
  Member "cyclic lrc codes and their subfield subcodes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "locally recoverable j affine variety codes")
  Member "weight enumerators and higher support weights of maximally recoverable codes":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "uniform minors in maximally recoverable codes")
  Member "locally recoverable codes on algebraic curves":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "new bounds on the field size for maximally recoverable codes instantiating grid like topologies")
  Member "repair locality from a combinatorial perspective":
    also connected through other hyperedges:
      - Hyperedge HE-6 (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")
  Member "codes with locality for two erasures":
    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 "an integer programming based bound for locally repairable codes":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "new bounds on the field size for maximally recoverable codes instantiating grid like topologies")

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)