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 ?

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    $\begingroup$ In coding theory written in English, it is almost universally true that $k$ denotes the number of information symbols and $d$ or $d_\min$ the minimum distance of the code. Please don't introduce a new nonstandard meaning for $k$. $\endgroup$ – Dilip Sarwate Apr 2 '19 at 13:43
  • $\begingroup$ @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. $\endgroup$ – Peter Shor May 5 '19 at 1:29
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    $\begingroup$ @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 $\endgroup$ – Bjørn Kjos-Hanssen May 5 '19 at 2:11

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