<p>Is there a way to compute minimum distance of a code given a systematic parity check matrix? I know that min dist is smallest number <span class="math-container">$d$</span> such that there exists <span class="math-container">$d$</span> linearly dependant columns. I am looking in particular to find minimum distance of binary (codes over <span class="math-container">$\mathbb{F}_{2^l}$</span>) quasi-cyclic  of rate q/q+1. Parity check matrix for such codes have a structure
<span class="math-container">$H=[I|C_1|C_2|...|C_m]$</span> where each <span class="math-container">$C_¡$</span> is a from class of circulant matrices. It may be useful that one can treat these codes as modules.
Or even if there are any approximate algoruihms for this ?</p>

CC BY-SA 4.0
2019-05-05T01:29:15.577Z
@Dilip: he's not introducing a new meaning for $k$; I don't see any variables named $k$ in his question. And he's using $d$ for minimum distance, which is perfectly standard.
Peter Shor 
CC BY-SA 4.0
2019-05-05T02:11:06.930Z
@PeterShor the $k$ was in the original post at math.stackexchange, and Dilip Sarwate's comment was on that version... so it became a non sequitur after migration
Bjørn Kjos-Hanssen
<coding-theory>
Minimum distance of a code
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# Minimum distance of a code

(Asked by: username_0 on 2019-04-02)

Is there a way to compute minimum distance of a code given a systematic parity check matrix? I know that min dist is smallest number $d$ such that there exists $d$ linearly dependant columns. I am looking in particular to find minimum distance of binary (codes over $\mathbb{F}\_{2^l}$) quasi-cyclic of rate q/q+1. Parity check matrix for such codes have a structure
$H=[I|C\_1|C\_2|...|C\_m]$ where each $C\_¡$ is a from class of circulant matrices. It may be useful that one can treat these codes as modules.
Or even if there are any approximate algoruihms for this ?

**Tags:** coding-theory
> **Comments:**
> **username_1**: @Dilip: he's not introducing a new meaning for $k$; I don't see any variables named $k$ in his question. And he's using $d$ for minimum distance, which is perfectly standard.  
> **username_2**: @PeterShor the $k$ was in the original post at math.stackexchange, and Dilip Sarwate's comment was on that version... so it became a non sequitur after migration  

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