scholarly journals Combinatorial Construction of Locally Testable Codes

2009 ◽  
Vol 39 (2) ◽  
pp. 491-544 ◽  
Author(s):  
Or Meir
Keyword(s):  
Locally Testable Codes ◽  
Combinatorial Construction

scholarly journals An Algorithm for Recognising the Exterior Square of a Multiset

2000 ◽  
Vol 3 ◽  
pp. 96-116 ◽  
Author(s):  
Catherine Greenhill
Keyword(s):  
Abelian Group ◽  
Vector Space ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Combinatorial Construction ◽  
Exterior Square

AbstractThe exterior square of a multiset is a natural combinatorial construction which is related to the exterior square of a vector space. We consider multisets of elements of an abelian group. Two properties are defined which a multiset may satisfy: recognisability and involution-recognisability. A polynomial-time algorithm is described which takes an input multiset and returns either (a) a multiset which is either recognisable or involution-recognisable and whose exterior square equals the input multiset, or (b) the message that no such multiset exists. The proportion of multisets which are neither recognisable nor involution-recognisable is shown to be small when the abelian group is finite but large. Some further comments are made about the motivating case of multisets of eigenvalues of matrices.

scholarly journals Overlapping Pfaffians

10.37236/1263 ◽  
1995 ◽  
Vol 3 (2) ◽  
Author(s):  
Donald E. Knuth
Keyword(s):  
Symmetric Matrix ◽  
History Of ◽  
Combinatorial Construction ◽  
Skew Symmetric Matrix

A combinatorial construction proves an identity for the product of the Pfaffian of a skew-symmetric matrix by the Pfaffian of one of its submatrices. Several applications of this identity are followed by a brief history of Pfaffians.

scholarly journals High-Rate Locally Correctable and Locally Testable Codes with Sub-Polynomial Query Complexity

2017 ◽  
Vol 64 (2) ◽  
pp. 1-42 ◽  
Author(s):  
Swastik Kopparty ◽  
Or Meir ◽  
Noga Ron-Zewi ◽  
Shubhangi Saraf
Keyword(s):  
High Rate ◽  
Query Complexity ◽  
Locally Testable Codes
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