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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.

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  • $\begingroup$ 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] $\endgroup$
    – kodlu
    Aug 12, 2022 at 14:54
  • $\begingroup$ 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. $\endgroup$
    – randomprime
    Aug 13, 2022 at 2:24

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