At the third section of a paper "Computing second cohomology of finite groups with trivial coefficients" by G. Ellis et al., the authors write
Suppose that $<\underline{x}\mid \underline{r}>=<x_1 \cdots x_d \mid r_1 \cdots r_m>$ is the presentation of the finite group $G$, so that $\underline{x}$ is a generating set for $F$ and $\underline{r}$ is a set of elements in $F$ that normally generate $R$. The function RelatorMatrix(F,rels), with rels := $\underline{r}$, uses the LLL algorithm to return integer matrices $B,T$.
In the above $F$ is free group such that $F/R=G$.
I have searched many times in google what is Relator matrix with integer coefficient. How to find integer matrix with given presentation. I find nothing. I will be thankful to you if you kindly tell me how to find these matrices or tell me the reference where I can find these.