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 dependence of linear coding rates on the characteristic of the finite field"):
  Abstract: It is known that for any finite/co-finite set of primes there exists a network which has a rate $1$ solution if and only if the characteristic of the finite field belongs to the given set. We generalize this result to show that for any positive rational number $k/n$, and for any given finite/co-finite set of primes, there exists a network which has a rate $k/n$ fractional linear network coding solution if and only if the characteristic of the finite field belongs to the given set. For this purpose we construct two networks: $\mathcal{N}_1$ and $\mathcal{N}_2$; the network $\mathcal{N}_1$ has a $k/n$ fractional linear network coding solution if and only if the characteristic of the finite field belongs to the given finite set of primes, and the network $\mathcal{N}_2$ has a $k/n$ fractional linear network coding solution if and only if the characteristic of the finite field belongs to the given co-finite set of primes. #R##N#Recently, a method has been introduced where characteristic-dependent linear rank inequalities are produced from networks whose linear coding capacity depends on the characteristic of the finite field. By employing this method on the networks $\mathcal{N}_1$ and $\mathcal{N}_2$, we construct two classes of characteristic-dependent linear rank inequalities. For any given set of primes, the first class contains an inequality which holds if the characteristic of the finite field does not belong to the given set of primes but may not hold otherwise; the second class contains an inequality which holds if the characteristic of the finite field belongs to the given set of primes but may not hold otherwise. We then use these inequalities to obtain an upper-bound on the linear coding capacity of $\mathcal{N}_1$ and $\mathcal{N}_2$.

Includes members:
  Member "linear network coding over rings part i scalar codes and commutative alphabets":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "linear network coding effects of varying the message dimension on the set of characteristics")
  Member "capacity and achievable rate regions for linear network coding over ring alphabets":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "linear network coding effects of varying the message dimension on the set of characteristics")
  Member "multicast network coding and field sizes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "linear network coding effects of varying the message dimension on the set of characteristics")
  Member "characteristic dependent linear rank inequalities with applications to network coding":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "characteristic dependent linear rank inequalities via complementary vector spaces")
  Member "achievable rate regions for network coding":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "characteristic dependent linear rank inequalities via complementary vector spaces")
  Member "on network coding for sum networks":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "linear network coding effects of varying the message dimension on the set of characteristics")

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)