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 "packing and covering properties of subspace codes for error control in random linear network coding"):
  Abstract: Codes in the projective space and codes in the Grassmannian over a finite field - referred to as subspace codes and constant-dimension codes (CDCs), respectively - have been proposed for error control in random linear network coding. For subspace codes and CDCs, a subspace metric was introduced to correct both errors and erasures, and an injection metric was proposed to correct adversarial errors. In this paper, we investigate the packing and covering properties of subspace codes with both metrics. We first determine some fundamental geometric properties of the projective space with both metrics. Using these properties, we then derive bounds on the cardinalities of packing and covering subspace codes, and determine the asymptotic rates of optimal packing and optimal covering subspace codes with both metrics. Our results not only provide guiding principles for the code design for error control in random linear network coding, but also illustrate the difference between the two metrics from a geometric perspective. In particular, our results show that optimal packing CDCs are optimal packing subspace codes up to a scalar for both metrics if and only if their dimension is half of their length (up to rounding). In this case, CDCs suffer from only limited rate loss as opposed to subspace codes with the same minimum distance. We also show that optimal covering CDCs can be used to construct asymptotically optimal covering subspace codes with the injection metric only.

Includes members:
  Member "recursive code construction for random networks":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "new constructions of subspace codes using subsets of mrd codes in several blocks")
  Member "construction and covering properties of constant dimension codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a new construction for constant weight codes")
  Member "on metrics for error correction in network coding":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "point line incidence on grassmannians and majority logic decoding of grassmann codes")
  Member "error correcting codes in projective spaces via rank metric codes and ferrers diagrams":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a note on echelon ferrers construction")
  Member "a rank metric approach to error control in random 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 "construction of large constant dimension codes with a prescribed minimum distance":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on some automorphisms of rational functions and their applications in rank metric codes")
  Member "bounds on covering codes with the rank metric":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "finite field matrix channels for network coding")
  Member "coding for errors and erasures in random network coding":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "on the gap between scalar and vector solutions of generalized combination networks")

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)