how to insert elements to get a new output

i have a character variable with elements such as

cv = '000001010011100101111'
vect = [1 2 3];

Now i want to insert the vect elements to cv after every 3 elements. So that i get

new_cv = '0001001201030111100210131111'

for understandability i insert space after 3 elements

cv = '000 001 010 011 100 101 111'
new_cv = '000 1 001 2 010 3 011 1 100 2 101 3 111 1'

The elements of vect is repeated till the length of cv

Answer 1

[Guillaume]

cv = '000001010011100101111'
vect = [1 2 3];
groupsize = 3;  

assert(mod(numel(cv), groupsize) == 0, 'Input cannot be divided evenly into groups of %d elements', groupsize);
prefix = reshape(cv, groupsize, []);  %reshape input into columns of groupsize elements
postfix = char(repmat(vect + '0', 1, ceil(size(prefix, 2)/groupsize)));  %replicate vect to be at least as long as prefix, and convert to char
postfix = postfix(1:size(prefix, 2));  %truncate unneeded elements
result = reshape([prefix; postfix], 1, [])  %concatenate and reshape into one row

Answer 2

[Andrei Bobrov]

cv = '000001010011100101111';
k = 3;

out = reshape([reshape(cv,k,[]);sprintf('%d',(rem(0:numel(cv)/k-1,k)+1)')],1,[]);