cally testable cyclic code ászló Babai, Amir Shpilka, Daniel Štefankov are no good families of ly-testable cyclic codes over q F Theorem: 2 q This talk Are there good cyclic codes ??? [Open Problem 9.2 in MacWilliams, Sloane ’77] Are there good locally-testable codes ?? [Goldreich, Sudan ’02]
Locally testable cyclic codes. L á szl ó Babai, Amir Shpilka, Daniel Š tefankovič. Are there good cyclic codes ??? [Open Problem 9.2 in MacWilliams, Sloane ’77]. Are there good locally-testable codes ??? [Goldreich, Sudan ’02]. Theorem:. There are no good families of - PowerPoint PPT Presentation
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Locally testable cyclic codes
László Babai, Amir Shpilka, Daniel Štefankovič
There are no good families of locally-testable cyclic codes over . qF
Theorem:
2q This talk
Are there good cyclic codes ???[Open Problem 9.2 in MacWilliams, Sloane ’77]
Are there good locally-testable codes ???[Goldreich, Sudan ’02]
alphabet size
minimum weight = distance
dimension = information length
block size
= linear subspace of
Linear codes – basic parameters
nqFCcode
kd
nq
A good family of codes
( )k nn
( )d n
existence [Shannon’48].explicit [Justesen’72].
linear information (const rate)linear distance ( errors corrected)
( )n
Cyclic codes [Prange’57]
0 1( ,..., )na a C 1 0 1 2( , , ,..., , )n na a a a C
Why cyclic codes?
0 1 1 0 1
[MacWilliams,Sloane’77] ”Cyclic codes are the most studiedof all codes since they are easy to encode and include the important family of BCH codes.”