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In this work we explore error-correcting codes derived from the "lifting" of "affine-invariant" codes. Affine-invariant codes are simply linear codes whose coordinates are a vector space over a field and which are invariant under affine-transformations of the coordinate space. Lifting takes codes defined over a vector space of small dimension and lifts them(More)
We prove NP-hardness results for five of Nintendo’s largest video game franchises: Mario, Donkey Kong, Legend of Zelda, Metroid, and Pokémon. Our results apply to generalized versions of Super Mario Bros. 1–3, The Lost Levels, and Super Mario World; Donkey Kong Country 1–3; all Legend of Zelda games; all Metroid games; and all Pokémon role-playing games. In(More)
We prove NP-hardness results for five of Nintendo’s largest video game franchises: Mario, Donkey Kong, Legend of Zelda, Metroid, and Pokémon. Our results apply to Super Mario Bros. 1, 3, Lost Levels, and Super Mario World; Donkey Kong Country 1–3; all Legend of Zelda games except Zelda II: The Adventure of Link; all Metroid games; and all Pokémon(More)
A local property reconstructor for a graph property is an algorithm which, given oracle access to the adjacency list of a graph that is “close” to having the property, provides oracle access to the adjacency matrix of a “correction” of the graph, i.e. a graph which has the property and is close to the given graph. For this model, we achieve local property(More)
  • Alan Guo
  • IEEE Transactions on Information Theory
  • 2013
We present a general framework for constructing high-rate error correcting codes that are locally correctable (and hence locally decodable if linear) with a sublinear number of queries, based on lifting codes with respect to functions on the coordinates. Our approach generalizes the lifting of affine-invariant codes (of Guo, Kopparty, and Sudan) and its(More)
We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these lattice games can be made particularly efficient for octal games, which we generalize to squarefree games. These additionally encompass all heap games in a natural setting, in which the Sprague–Grundy theorem for(More)
A non-crossing connected graph is a connected graph on vertices arranged in a circle such that its edges do not cross. The count for such graphs can be made naturally into a q-binomial generating function. We prove that this generating function exhibits the cyclic sieving phenomenon, as conjectured by S.-P. Eu. Résumé. Un graphe connexe dont les sommets(More)
Lifted Reed-Solomon codes are a natural affine-invariant family of error-correcting codes, which generalize Reed-Muller codes. They were known to have efficient local-testing and local-decoding algorithms (comparable with the known algorithms for Reed-Muller codes), but with significantly better rate. We give efficient algorithms for list decoding and local(More)
We consider the homogeneous components Ur of the map on R = k[x, y, z]/(xA, yB , zC) that multiplies by x + y + z. We prove a relationship between the Smith normal forms of submatrices of an arbitrary Toeplitz matrix using Schur polynomials, and use this to give a relationship between Smith normal form entries of Ur. We also give a bijective proof of an(More)
OBJECTIVE To determine whether senior surgical residents can independently interpret radiologic studies for the trauma patients under their care. METHOD Five senior surgical residents (PGY-4 and -5) participated in this prospective study. The residents independently read trauma films as part of the emergency assessment, documenting their interpretations(More)