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 "construction of optimal locally recoverable codes and connection with hypergraph"):
  Abstract: Recently, it was discovered by several authors that a $q$-ary optimal locally recoverable code, i.e., a locally recoverable code archiving the Singleton-type bound, can have length much bigger than $q+1$. This is quite different from the classical $q$-ary MDS codes where it is conjectured that the code length is upper bounded by $q+1$ (or $q+2$ for some special case). This discovery inspired some recent studies on length of an optimal locally recoverable code. It was shown in \cite{LXY} that a $q$-ary optimal locally recoverable code is unbounded for $d=3,4$. Soon after, it was proved that a $q$-ary optimal locally recoverable code with distance $d$ and locality $r$ can have length $\Omega_{d,r}(q^{1 + 1/\lfloor(d-3)/2\rfloor})$. Recently, an explicit construction of $q$-ary optimal locally recoverable codes for distance $d=5,6$ was given in \cite{J18} and \cite{BCGLP}. #R##N#In this paper, we further investigate construction optimal locally recoverable codes along the line of using parity-check matrices. Inspired by classical Reed-Solomon codes and \cite{J18}, we equip parity-check matrices with the Vandermond structure. It is turns out that a parity-check matrix with the Vandermond structure produces an optimal locally recoverable code must obey certain disjoint property for subsets of $\mathbb{F}_q$. To our surprise, this disjoint condition is equivalent to a well-studied problem in extremal graph theory. With the help of extremal graph theory, we succeed to improve all of the best known results in \cite{GXY} for $d\geq 7$. In addition, for $d=6$, we are able to remove the constraint required in \cite{J18} that $q$ is even.

Includes members:
  Member "how long can optimal locally repairable codes be":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes")
  Member "explicit construction of optimal locally recoverable codes of distance 5 and 6 via binary constant weight codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes")
  Member "optimal locally repairable codes of distance 3 and 4 via cyclic codes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "constructive asymptotic bounds of locally repairable codes via function fields")
  Member "locally recoverable codes from algebraic curves and surfaces":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "convertible codes efficient conversion of coded data in distributed storage")
  Member "a family of optimal locally recoverable codes":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a locality based approach for coded computation")
  Member "optimal locally repairable codes and connections to matroid theory":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes")
  Member "optimal linear codes with a local error correction property":
    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)