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 "binary linear locally repairable codes"):
  Abstract: Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do not explicitly take into consideration the field size $q$, i.e., the size of the code alphabet. In particular, for the binary case, only a few results are known. #R##N#In this work, we present an upper bound on the minimum distance $d$ of linear LRCs with availability, based on the work of Cadambe and Mazumdar. The bound takes into account the code length $n$, dimension $k$, locality $r$, availability $t$, and field size $q$. Then, we study binary linear LRCs in three aspects. First, we focus on analyzing the locality of some classical codes, i.e., cyclic codes and Reed-Muller codes, and their modified versions, which are obtained by applying the operations of extend, shorten, expurgate, augment, and lengthen. Next, we construct LRCs using phantom parity-check symbols and multi-level tensor product structure, respectively. Compared to other previous constructions of binary LRCs with fixed locality or minimum distance, our construction is much more flexible in terms of code parameters, and gives various families of high-rate LRCs, some of which are shown to be optimal with respect to their minimum distance. Finally, availability of LRCs is studied. We investigate the locality and availability properties of several classes of one-step majority-logic decodable codes, including cyclic simplex codes, cyclic difference-set codes, and $4$-cycle free regular low-density parity-check (LDPC) codes. We also show the construction of a long LRC with availability from a short one-step majority-logic decodable code.

Includes members:
  Member "optimal linear and cyclic locally repairable codes over small fields":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the complete hierarchical locality of the punctured simplex code")
  Member "optimal binary locally repairable codes via anticodes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "new bounds on the field size for maximally recoverable codes instantiating grid like topologies")
  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 "repair locality with multiple erasure tolerance":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes")
  Member "repairable fountain codes":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "locally repairable convolutional codes with sliding window repair")
  Member "constructions of optimal and almost optimal locally repairable codes":
    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 "locality and availability in distributed storage":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes")
  Member "codes with locality for two erasures":
    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)