Locally decodable code

A locally decodable code is like a secret code that only certain people can read. If you want to send a secret message to someone, you can put your message into this code. But instead of sending the whole code, you only send a small part of it. This small part is called a "query."

The person receiving the message will use this query to decode the secret message, without needing to see the entire code. Like a magic trick, they will be able to figure out what the message is just by looking at this small part of the code.

Now, you might be thinking, "Why would I use this locally decodable code instead of just sending the secret message directly?" The answer is that encoding and decoding this code uses a lot of computer power. It's like solving a really hard puzzle. But with a locally decodable code, you only have to solve a small part of the puzzle. This is much faster and easier than solving the entire puzzle.

In fact, this locally decodable code is so smart that even if some of the bits in the code are changed during transmission (maybe there was a little bit of static on the phone line), the person receiving the message can still figure out the secret message with just a few queries. This makes it really useful for sending important messages that can't afford to get lost or changed.

TL;DR: A locally decodable code is like a secret code that only certain people can read. You only send a small part of it, and the person receiving the message can decode the secret message easily, even if some bits are changed.