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Linear Block Coding: Enclosure property of codeword space

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neoflash

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In Skalar's book, he stated that there is two rules to be followed for a sub-space.

That a subspace need to contains all zero and it is required to be enclosure.

Why?
 

Re: Linear Block Coding: Enclosure property of codeword spac

What is the main part of your question ?
Why a subspace need to contain all zero code vector or why it must be closed under sum operation?
Property of closed operation under summation with property of scalar multiplication gives an opportunity to form all code vectors using generator matrix (basis vector’s )( look in 6.4.4 of Scalar).
I suppose zero code word needed because Vi+Vi must also be in subspace (it is so called "identity" element under addition in "group").
 

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    neoflash

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i agree on first part.

However, on second part, i think it is the same as your answer to the first question, the all-zero message will generate a all-zero code-word anyway.
 

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