Locally testable code: Difference between revisions

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Added "See also" section with link to Gilbert–Varshamov bound
Added definition of the rate of a code
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:* For any <math>x\in\{0,1\}^k</math> and <math>w=C(x)</math>, <math>Pr[M^w(1^k)=1]=1</math>. In other words, M accepts given access to any codeword of C.
:* For <math>w\in\{0,1\}^n</math> such that <math>\delta(w,C)>\delta</math>, <math>Pr[M^w(1^k)=1]\leq1/2</math>. M must reject strings <math>\delta</math>-far from C at least half the time.
Also the rate of the code is the ratio between the message length and codeword length
:<math> r=\frac{|x|}{|C(x)|}</math>
 
== Limits ==