Optimal Lower Bounds for 2-Query Locally Decodable Linear Codes

2002 ◽  
pp. 39-50 ◽  
Author(s):  
Kenji Obata
Keyword(s):  
Lower Bounds ◽  
Linear Codes ◽  
Locally Decodable

Circuit lower bounds and linear codes

2006 ◽  
Vol 134 (5) ◽  
pp. 2425-2434 ◽  
Author(s):  
R. Paturi ◽  
P. Pudlák
Keyword(s):  
Lower Bounds ◽  
Linear Codes ◽  
Circuit Lower Bounds

QUASI-CYCLIC CODES FROM CYCLIC-STRUCTURED DESIGNS WITH GOOD PROPERTIES

2011 ◽  
Vol 03 (02) ◽  
pp. 223-243
Author(s):  
CHRISTOS KOUKOUVINOS ◽  
DIMITRIS E. SIMOS
Keyword(s):  
Lower Bounds ◽  
Minimum Distance ◽  
Optimization Problem ◽  
Linear Codes ◽  
Cyclic Codes ◽  
Mathematical Structure ◽  
Combinatorial Optimization Problem ◽  
Supersaturated Designs ◽  
Statistical Designs ◽  
Quasi Cyclic Codes

In this paper, one-generator binary quasi-cyclic (QC) codes are explored by statistical tools derived from design of experiments. A connection between a structured cyclic class of statistical designs, k-circulant supersaturated designs and QC codes is given. The mathematical structure of the later codes is explored and a link between complementary dual binary QC codes and E(s2)-optimal k-circulant supersaturated designs is established. Moreover, binary QC codes of rate 1/3, 1/4, 1/5, 1/6 and 1/7 are found by utilizing a genetic algorithm. Our approach is based on a search for good or best codes that attain the current best-known lower bounds on the minimum distance of linear codes, formulated as a combinatorial optimization problem. Surveying previous results, it is shown, that our codes reach the current best-known lower bounds on the minimum distance of linear codes with the same parameters.

An optimal lower bound for 2-query locally decodable linear codes

2006 ◽  
Vol 97 (6) ◽  
pp. 244-250 ◽  
Author(s):  
Dungjade Shiowattana ◽  
Satyanarayana V. Lokam
Keyword(s):  
Lower Bound ◽  
Linear Codes ◽  
Locally Decodable ◽  
Optimal Lower Bound

Better lower bounds for locally decodable codes

2003 ◽  
Author(s):  
A. Deshpande ◽  
R. Jain ◽  
T. Kavitha ◽  
S.V. Lokam ◽  
J. Radhakrishnan
Keyword(s):  
Lower Bounds ◽  
Locally Decodable Codes ◽  
Locally Decodable
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