Thread by @LGcommaI

#GoldreichTestableCodesSurvey-4

"Codes, proofs and their length
Codes are sets of strings (of equal length), typically, having a large pairwise distance. Equivalently, codes are viewed as mappings from short (𝑘-bit) strings to longer (𝑛-bit) strings, called codewords,
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>such that the codewords are distant from one another. We will focus on codes with relative constant distance; that is, every two 𝑛-bit codewords are at distance Ω(𝑛) apart. The length of the code is measured in terms of the length of the pre-image (i.e., we are interested
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>in the growth of 𝑛 as a function of 𝑘).
Turning to proofs, these are defined with respect to a verification procedure for assertions of a certain length, and their length is measured in terms of the length of the assertion. The verification procedure must satisfy the natural
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>completeness and soundness properties: For valid assertions there should be strings, called proofs, that are accepted (in conjunction with the assertion) by the verification procedures, whereas for false assertions no such strings may exist. The reader may envision
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>proof systems for the set of satisfiable propositional formulae (i.e., assertions of satisfiability of given formulae)."

M.t. 'Codes, Beweise und ihre Länge.
Codes sind Mengen von Zeichenketten (gleicher Länge), typischerweise mit großem paarweisem Abstand. Gleichwertig dazu:
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