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 "linear network coding effects of varying the message dimension on the set of characteristics"):
  Abstract: It is known a vector linear solution may exist if and only if the characteristic of the finite field belongs to a certain set of primes. But, can increasing the message dimension make a network vector linearly solvable over a larger set of characteristics? To the best of our knowledge, there exists no network in the literature which has a vector linear solution for some message dimension if and only if the characteristic of the finite field belongs to a set $P$, and for some other message dimension it has a vector linear solution over some finite field whose characteristic does not belong to $P$. We have found that by \textit{increasing} the message dimension just by $1$, the set of characteristics over which a vector linear solution exists may get arbitrarily larger. However, somewhat surprisingly, we have also found that by \textit{decreasing} the message dimension just by $1$, the set of characteristics over which a vector linear solution exists may get arbitrarily larger. #R##N#As a consequence of these finding, we prove two more results: (i) rings may be superior to finite fields in terms of achieving a scalar linear solution over a lesser sized alphabet, (ii) existences of $m_1$ and $m_2$ dimensional vector linear solutions guarantees the existence of an $(m_1 + m_2)$-dimensional vector linear solution only if the $m_1$ and $m_2$ dimensional vector linear solutions exist over the same finite 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 "circular shift linear network codes with arbitrary odd block lengths")
  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 "capacity achieving private information retrieval codes with optimal message size and upload cost")
  Member "capacity and achievable rate regions for linear network coding over ring alphabets":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on the dependence of linear coding rates on the characteristic of the finite field")
  Member "on the message dimensions of vector linearly solvable networks":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "circular shift linear network codes with arbitrary odd block lengths")
  Member "on base field of linear network coding":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "linear network coding over rings part i scalar codes and commutative alphabets")
  Member "on vector linear solvability of multicast networks":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on the gap between scalar and vector solutions of generalized combination networks")
  Member "vector network coding based on subspace codes outperforms scalar linear network coding":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "roos bound for skew cyclic codes in hamming and rank metric")
  Member "multicast network coding and field sizes":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "circular shift linear network coding")

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)