Linear Codes with Exponentially Many Light Vectors
نویسندگان
چکیده
منابع مشابه
Linear Codes with Exponentially Many Light Vectors
Let C be a code over q of length n and distance d = d(C): The (Hamming) distance distribution of the code is an (n + 1)-vector (A0 = 1; A1; : : : ; An); where Aw = Aw(C) := (]C) 1jf(x; x0) 2 C : d(x; x0) = wgj: Of course Aw = 0 if 1 w d 1: Let fCng be a family of binary linear codes of growing length n and let dn = d(Cn): G. Kalai and N. Linial [2] conjectured that for any such family the numbe...
متن کاملExponentially many supertrees
The amalgamation of leaf-labelled trees into a single supertree that displays each of the input trees is an important problem in classification. Clearly, there can be more than one (super) tree for a given set of input trees, in particular if a highly unresolved supertree exists. Here, we show (by explicit construction) that even if every supertree of a given collection of input trees is binary...
متن کاملAre Quantum States Exponentially Long Vectors?
I’m grateful to Oded Goldreich for inviting me to the 2005 Oberwolfach Meeting on Complexity Theory. In this extended abstract, which is based on a talk that I gave there, I demonstrate that gratitude by explaining why Goldreich’s views about quantum computing are wrong. Why should anyone care? Because in my opinion, Goldreich, along with Leonid Levin [10] and other “extreme” quantum computing ...
متن کاملAssociative content-addressable networks with exponentially many robust stable states
The brain must robustly store a large number of memories, corresponding to the many events and scenes a person encounters over a lifetime. However, the number of memory states in existing neural network models either grows weakly with network size or recall performance fails catastrophically with vanishingly little noise. Here we show that it is possible to construct an associative content-addr...
متن کاملRank-1 Games With Exponentially Many Nash Equilibria
The rank of a bimatrix game (A,B) is the rank of the matrix A + B. We give a construction of rank-1 games with exponentially many equilibria, which answers an open problem by Kannan and Theobald (2010).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2001
ISSN: 0097-3165
DOI: 10.1006/jcta.2001.3206