In the first part of today’s lecture, we proved the following general result. Any linear code with dual distance at least , is an -wise independent source. As a corollary, we saw that the dual of the code is an -wise independent source of size .

Next, we returned to the question of an explicit asymptotically good code. The best construction we have seen so far is the trivial conversion of a RS code over into a binary code using any map . We finally observed that we need to replace by a code with large distance. Next lecture, we will see a general code composition technique called *code concatenation* that does exactly this.

In the lecture today, I totally messed up the statement of the Weil-Carlitz-Uchiyama bound. Here is the correct statement: Any non-zero codewords in the dual of the has Hamming weight such that

provided .

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