# Is there a name/terminology for binary codes with evenly spaced number of ones?

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.

• 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] Commented Aug 12, 2022 at 14:54
• 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. Commented Aug 13, 2022 at 2:24