<p>I am generating a random binary matrix <span class="math-container">$A \in \{0, 1\}^{m \times n}$</span> with the number of ones in each row set to evenly spaced numbers from an interval. For example, if <span class="math-container">$n=50$</span>, the number of ones for <span class="math-container">$m=5$</span> rows will be equal to <span class="math-container">$[ 1, 12, 25, 37, 50]$</span> i.e. <span class="math-container">$A$</span> will be a matrix with first row containing a single one, second row containing 12 ones, third containing 25 ones and so on. I was wondering if this style of construction is well-known and if there is a class of binary codes that it corresponds to?</p>
<p>Thank you for your help.</p>

CC BY-SA 4.0
2022-08-12T14:54:26.307Z
are those numbers "evenly" spaced? define what you want. I see differences of 11, 13, 12, 13 in the sequence [1,12,25,37,50]
kodlu
CC BY-SA 4.0
2022-08-13T02:24:58.203Z
Thank you! probably the better word would be equally spread out? In the example, I want to keep adding ones so that it sum ups to n in the last row but if it helps figuring out some connection, considering exactly same numbers like [1, 12, 23, 34, 45] also works for me.
randomprime
<boolean-functions><it.information-theory><coding-theory><embeddings><boolean-matrix>
Is there a name/terminology for binary codes with evenly spaced number of ones?
randomprime
# Is there a name/terminology for binary codes with evenly spaced number of ones?

(Asked by: username_0 on 2022-08-08)

I am generating a random binary matrix $A \in \{0, 1\}^{m \times n}$ with the number of ones in each row set to evenly spaced numbers from an interval. For example, if $n=50$, the number of ones for $m=5$ rows will be equal to $[ 1, 12, 25, 37, 50]$ i.e. $A$ will be a matrix with first row containing a single one, second row containing 12 ones, third containing 25 ones and so on. I was wondering if this style of construction is well-known and if there is a class of binary codes that it corresponds to?

Thank you for your help.

**Tags:** boolean-functions, it.information-theory, coding-theory, embeddings, boolean-matrix

> **Comments:**
> **username_1**: are those numbers "evenly" spaced? define what you want. I see differences of 11, 13, 12, 13 in the sequence [1,12,25,37,50]  
> **username_0**: Thank you! probably the better word would be equally spread out? In the example, I want to keep adding ones so that it sum ups to n in the last row but if it helps figuring out some connection, considering exactly same numbers like [1, 12, 23, 34, 45] also works for me.  

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## 0 answers

