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 "decoding high rate reed muller codes from random errors in near linear time"):
  Abstract: Reed-Muller codes encode an $m$-variate polynomial of degree $k$ by evaluating it on all points in $\{0,1\}^m$. We denote this code by $RM(m,k)$. For $k=m-r$, its distance is $2^r$ and so it cannot correct more than $2^{r-1}$ errors in the worst case. For random errors one may hope for a better result. Shannon (1948) proved that for codes of the same rate, one cannot correct more than roughly $m^r$ random errors and that there are codes that can correct that many errors. Abbe, Shpilka and Wigderson (2015) showed that about $m^{r/2}$ errors can be corrected for $RM(m,m-r)$, but their result was existential and did not give a decoding algorithm. In this work we give a near linear time algorithm (in the encoding length $n=2^m$) for decoding that many errors. #R##N#Our algorithm works correctly whenever the error locations satisfy some independence criterion. Using a result of Abbe et al. we get in particular that with high probability over the errors, our algorithm can correct $(1-o(1)){m\choose\leq r}$ random errors in $RM(m,m-(2r+2))$, when $r=O(\sqrt{m/\log m})$. This number of errors is much larger than the distance of the code, $2^{2r+2}$. #R##N#The algorithm is based on solving a carefully defined set of linear equations and thus it is significantly different than other algorithms for decoding Reed-Muller codes. It can be seen as a more explicit proof of the result of Abbe et al. for high rate Reed-Muller codes and it also bares some similarities with the Berlekamp-Welch algorithm for decoding Reed-Solomon codes. #R##N#Furthermore, the proof shows that for any $r$, our algorithm can correct any error pattern in $RM(m,m-(2r+2))$ for which the same erasure pattern can be corrected in $RM(m,m-(r+1))$. Thus if $RM(m,m-(r+1))$ achieves capacity for the Binary Erasure Channel, our algorithm can correct $1-o(1)$ fraction of error patterns of weight $(1-o(1)){m\choose \leq r}$ in $RM(m,m-(2r+2))$.

Includes members:
  Member "recursive decoding and its performance for low rate reed muller codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "reed muller codes theory and algorithms")
  Member "reed muller codes achieve capacity on erasure channels":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "partially symmetric monomial codes")
  Member "reed muller codes achieve capacity on the binary erasure channel under map decoding":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "repairing generalized reed muller codes")
  Member "reed muller codes for random erasures and errors":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "reed muller codes theory and algorithms")
  Member "list decoding reed muller codes over small fields":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "generalized list decoding")
  Member "from polar to reed muller codes a technique to improve the finite length performance":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "polar codes and their quantum domain counterparts")
  Member "channel coding the road to channel capacity":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "optimal constant weight codes under l_1 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)