Canonical matrices with entries integers modulo p

Abstract

The work considers an equivalence relation in the set of all $n\times m$ matrices with entries in the set $[p]=\{0,1,\dots ,p-1\}$. In each element of the factor-set generated by this relation, we define the concept of canonical matrix, namely the minimal element with respect to the lexicographic order. We have found a necessary and sufficient condition for an arbitrary matrix with entries in the set $[p]$ to be canonical. For this purpose, the matrices are uniquely represented by ordered n-tuples of integers.

arXiv admin note: text overlap with arXiv:1604.02714