L6_2

# An exhaustive search shows that the minimum n is 7

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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 is: 0000000 0101010 1010010 1111000 1100001 1001011 0110011 0011001 1100110 1001100 0110100 0011110 0000111 0101101 1010101 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 is the...
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## This document was uploaded on 02/26/2014 for the course CS 6.02 at MIT.

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