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 "capacity and achievable rate regions for linear network coding over ring alphabets"):
  Abstract: The rate of a network code is the ratio of the block size of the network's messages to that of its edge codewords. We compare the linear capacities and achievable rate regions of networks using finite field alphabets to the more general cases of arbitrary ring and module alphabets. For non-commutative rings, two-sided linearity is allowed. Specifically, we prove the following for directed acyclic networks: #R##N#(i) The linear rate region and the linear capacity of any network over a finite field depend only on the characteristic of the field. Furthermore, any two fields with different characteristics yield different linear capacities for at least one network. #R##N#(ii) Whenever the characteristic of a given finite field divides the size of a given finite ring, each network's linear rate region over the ring is contained in its linear rate region over the field. Thus, any network's linear capacity over a field is at least its linear capacity over any other ring of the same size. An analogous result also holds for linear network codes over module alphabets. #R##N#(iii) Whenever the characteristic of a given finite field does not divide the size of a given finite ring, there is some network whose linear capacity over the ring is strictly greater than its linear capacity over the field. Thus, for any finite field, there always exist rings over which some networks have higher linear capacities than over the field.

Includes members:
  Member "linear network coding over rings part ii vector codes and non 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 "linear network coding over rings part i scalar codes and commutative 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 "a class of non linearly solvable networks":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a local perspective on the edge removal problem")
  Member "on vector linear solvability of multicast networks":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the gap between scalar and vector solutions of generalized combination networks")
  Member "on achievability of an r l fractional linear network code":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "sum networks dependency on characteristic of the finite field under linear network coding")
  Member "the two unicast problem":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "linear network coding for two unicast z networks a commutative algebraic perspective and fundamental limits")
  Member "characteristic dependent linear rank inequalities with applications to network coding":
    also connected through other hyperedges:
      - Hyperedge HE-7 (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-8 (induced by source paper "characteristic dependent linear rank inequalities via complementary vector spaces")

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)