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 "coding theory and projective spaces"):
  Abstract: The projective space of order $n$ over a finite field $\F_q$ is a set of all subspaces of the vector space $\F_q^{n}$. In this work, we consider error-correcting codes in the projective space, focusing mainly on constant dimension codes. We start with the different representations of subspaces in the projective space. These representations involve matrices in reduced row echelon form, associated binary vectors, and Ferrers diagrams. Based on these representations, we provide a new formula for the computation of the distance between any two subspaces in the projective space. We examine lifted maximum rank distance (MRD) codes, which are nearly optimal constant dimension codes. We prove that a lifted MRD code can be represented in such a way that it forms a block design known as a transversal design. The incidence matrix of the transversal design derived from a lifted MRD code can be viewed as a parity-check matrix of a linear code in the Hamming space. We find the properties of these codes which can be viewed also as LDPC codes. We present new bounds and constructions for constant dimension codes. First, we present a multilevel construction for constant dimension codes, which can be viewed as a generalization of a lifted MRD codes construction. This construction is based on a new type of rank-metric codes, called Ferrers diagram rank-metric codes. Then we derive upper bounds on the size of constant dimension codes which contain the lifted MRD code, and provide a construction for two families of codes, that attain these upper bounds. We generalize the well-known concept of a punctured code for a code in the projective space to obtain large codes which are not constant dimension. We present efficient enumerative encoding and decoding techniques for the Grassmannian. Finally we describe a search method for constant dimension lexicodes.

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 "enumerative encoding in the grassmannian space":
    also connected through other hyperedges:
      (none)
  Member "on metrics for error correction in network coding":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "point line incidence on grassmannians and majority logic decoding of grassmann codes")
  Member "projective space codes for the injection metric":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "matrix codes as ideals for grassmannian codes and their weight properties")
  Member "packing and covering properties of subspace codes for error control in random linear network coding":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "list and probabilistic unique decoding of folded subspace codes")
  Member "construction of error correcting codes for random network coding":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "new improvements on the echelon ferrers construction")
  Member "spread codes and spread decoding in network coding":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "symbol erasure correction capability of spread codes")
  Member "a rank metric approach to error control in random 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")

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)