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 over rings part i scalar codes and commutative alphabets"):
  Abstract: Linear network coding over finite fields is a well-studied problem. We consider the more general setting of linear coding for directed acyclic networks with finite commutative ring alphabets. Our results imply that for scalar linear network coding over commutative rings, fields can always be used when the alphabet size is flexible, but other rings may be needed when the alphabet size is fixed. We prove that if a network has a scalar linear solution over some finite commutative ring, then the (unique) smallest such commutative ring is a field. We also show that fixed-size commutative rings are quasi-ordered, such that all the scalar linearly solvable networks over any given ring are also scalar linearly solvable over any higher-ordered ring. We study commutative rings that are maximal with respect to this quasi-order, as they may be considered the best commutative rings of a given size. We prove that a commutative ring is maximal if and only if some network is scalar linearly solvable over the ring, but not over any other commutative ring of the same size. Furthermore, we show that maximal commutative rings are direct products of certain fields specified by the integer partitions of the prime factor multiplicities of the ring’s size. Finally, we prove that there is a unique maximal commutative ring of size    $m$    if and only if each prime factor of    $m$    has multiplicity in {1, 2, 3, 4, 6}. As consequences, 1) every finite field is such a maximal ring and 2) for each prime    $p$   , some network is scalar linearly solvable over a commutative ring of size    $p^{k}$    but not over the field of the same size if and only if    $k \not \in \{1,2,3,4,6\}$   .

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 "a class of non linearly solvable networks":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a local perspective on the edge removal problem")
  Member "on base field of linear network coding":
    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 "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 "vector network coding based on subspace codes outperforms scalar linear network coding":
    also connected through other hyperedges:
      - Hyperedge HE-5 (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-6 (induced by source paper "linear network coding effects of varying the message dimension on the set of characteristics")
  Member "an equivalence between network coding and index coding":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "embedded index 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)