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Unformatted text preview: that the receiver can correct all single-bit errors in the received words.
Clearly, we need to ﬁnd a set of messages S with 24 elements. Quick, what should the
members of S be?
The answer isn’t obvious. Once again, we could write a program to search through
possible sets of n-bit messages until it ﬁnds a set of size 16 with a minimum Hamming
distance of 3. An exhaustive search shows that the minimum n is 7, and one example of S
1111111 But such exhaustive searches are impractical when we want to send even modestly
longer messages. So we’d like some constructive technique for building S . Much of the
theory and practice of coding is devoted to ﬁnding such constructions and developing
efﬁcient encoding and decoding strategies.
Broadly speaking, there are two classes of code constructions, each with an enormous
number of example instances. The ﬁrst is the class of algebraic block codes. The second
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This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.
- Fall '13