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If no two strings in a code differ in fewer than three positions, the we can actually correct a single error, by finding the unique string in the code that differs from the received string in only one position. It turns out that there is a code of 7-bit strings that corrects single errors and contains 16 strings. Find such a code.

Hint: Reasoning it out is probably best, but if you get stuck, write a program that searches for the string.

From the example in the book - the strings would be like ASCII sequence of bits - whereby ASCII has a seven bit code and then a parity bit placed on the front for error detecting.

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Solution Summary

The solution shows how to find a code with the given string characteristics.

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The code of length n = 7 bits (with a total of 16 strings or codewords) that can detect and correct a single error bit can be found as

1st string ...

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