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.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Shortening LInear Codes

Loading...

Similar Threads - Shortening LInear Codes | Date |
---|---|

I Solutions to equations involving linear transformations | Mar 6, 2018 |

I Geometric intuition of a rank formula | Feb 8, 2018 |

I Tensors vs linear algebra | Jan 28, 2018 |

I Is there a geometric interpretation of orthogonal functions? | Jan 25, 2018 |

Proof that all information can be coded in binary? | Aug 15, 2015 |

**Physics Forums - The Fusion of Science and Community**