I'm not sure if this is the right forum for this question, but it is a form of linear algebra, so I'll give it a shot. It's about coding theory.(adsbygoogle = window.adsbygoogle || []).push({});

The problem is given a q-ary [n,k,d] linear code, fix an arbitrary column number and then collect all the code words that have 0 in that column. Make a new code from these words by deleting this column.

Show that this new code is a linear [n-1, k', d'] code, where k'=k or k'=k-1 and d'>=d.

Showing it is a linear code was easy.

Showing it was n-1 was also easy, as was the constraints on d'.

However, I can't see a good way to show the constraints on k'. I have an intuitive understanding of why this is true, but I can't figure out how to formulate it rigorously.

I can find a proof for binary codes in a round about way, but I don't see a trivial way to generalize it to other fields.

Any tips would be appreciated.

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# Shortening LInear Codes

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