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 "index coding rank invariant extensions"):
  Abstract: An index coding (IC) problem consisting of a server and multiple receivers with different side-information and demand sets can be equivalently represented using a fitting matrix. A scalar linear index code to a given IC problem is a matrix representing the transmitted linear combinations of the message symbols. The length of an index code is then the number of transmissions (or equivalently, the number of rows in the index code). An IC problem ${\cal I}_{ext}$ is called an extension of another IC problem ${\cal I}$ if the fitting matrix of ${\cal I}$ is a submatrix of the fitting matrix of ${\cal I}_{ext}$. We first present a straightforward $m$\textit{-order} extension ${\cal I}_{ext}$ of an IC problem ${\cal I}$ for which an index code is obtained by concatenating $m$ copies of an index code of ${\cal I}$. The length of the codes is the same for both ${\cal I}$ and ${\cal I}_{ext}$, and if the index code for ${\cal I}$ has optimal length then so does the extended code for ${\cal I}_{ext}$. More generally, an extended IC problem of ${\cal I}$ having the same optimal length as ${\cal I}$ is said to be a \textit{rank-invariant} extension of ${\cal I}$. We then focus on $2$-order rank-invariant extensions of ${\cal I}$, and present constructions of such extensions based on involutory permutation matrices.

Includes members:
  Member "uniprior index coding":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "linear codes for broadcasting with noisy side information")
  Member "structural properties of index coding capacity":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on index coding for complementary graphs with focus on circular perfect graphs")
  Member "the single uniprior index coding problem the single sender case and the multi sender extension":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "secure decentralized pliable index coding")
  Member "structural properties of index coding capacity using fractional graph theory":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "cooperative multi sender index coding")
  Member "optimal vector linear index codes for some symmetric side information problems":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "linear codes for broadcasting with noisy side information")
  Member "on a duality between recoverable distributed storage and index coding":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "embedded index coding")
  Member "topological interference management through index coding":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "on the separability of parallel miso broadcast channels under partial csit a degrees of freedom region perspective")
  Member "on index coding and graph homomorphism":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "the single uniprior index coding problem the single sender case and the multi sender extension")

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)