Quiz 7 - Polynomial Commitments based on Error-correcting Codes
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10 points
PC schemes based on error-correcting codes can be field-agnostic unlike KZG and Bulletproofs
We need codes with asymptotically good relative distance to construct polynomial commitment schemes
Reed-Solomon codes are linear-time encodable codes
PC schemes based on error-correcting codes have large proof sizes
The matrix vector product r * F can be a codeword even if the rows of the coefficient matrix F are not all codewords
In the PC scheme discussed in the lecture, the prover cannot pass the proximity test if it commits to a coefficient matrix F with rows that are not codewords
In the matrix vector argument, the proximity and consistency tests check inner product consistency against the same set of columns of the coefficient matrix F
The PC scheme discussed in the lecture does not require a code with efficient decoding
Lossless expander graphs help us build codes with constant relative distance because each vertex in the left part connects to a constant fraction of nodes in the right part
In the linear-time encodable code constructed using expander graphs, the distance Delta' does not depend on parameter beta of the expander graph
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