1-Define the product, , of two binary vectors of the same length to be the vector whose ith component is the product of the ith components of and .
Show that wt ( + ) =wt ( ) +wt ( ) - 2wt ( ) . wt means weight.

2. Suppose that a binary Hamming code is modified by adding an additional check bit to each codeword. This additional check bit is chosen so that each resulting vector has even weight.

a) Show that this procedure yields a linear code. You can use problem 1 to solve this part.
b) What are the parameter [n, k, d] of this new code? Prove your assertions, in particular for d.
c) How many errors can this new code correct?
d) How many errors can this new code detect, but not necessarily correct?
Note: This new code is called the extended Hamming code. Can you explain this definition

Can you give a specific example to understand this problem.

Please see the attached file for the fully formatted problems.

The Binary Hamming code is investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

...Coding of Binary Information and Error Detection (XI) Group Code of an Encoding Function ... The Hamming distance between and is the weight , of ... iii) Code Word Let ...

... (Hint: For binary strings a and b, the Hamming distance is ... Because we weren't given binary codes for spaces and because the two strings above don't look like ...

...Coding of Binary Information and Error Detection (VI) Minimum Distance of the Encoding ... The Hamming distance between and is the weight , of . ... iii) Code Word Let ...

Devise a code set for the digits 0 to 9 that has ... The hamming distance is the number of differences in bits ... So we first write the binary code for digits 0 and 9 ...

... Show the bit sequence transmitted (in binary) for the four-character frame: AB ESC FLAG when each of the ... What is the Hamming distance of this code? ...

...Coding of Binary Information and Error Detection (IX) Minimum Distance of the Encoding ... The Hamming distance between and is the weight , of . ... iii) Code Word Let ...

... can develop a similar expression to one noting that the number n of binary bits can ... 5. In a Hamming code, some bits are wasted in the sense that they are ...

... Income was constructed as a binary mea- family able to ... Data Analysis Item responses were reverse coded as necessary ... 1. Shochet IM, Dadds MR, Ham D, Montague R ...

... a) How many check bits are needed if the Hamming error correction code is used ... it take to obtain as many combinations as can be done with 10 binary digits ...