Rank and Pairs of Rank and Dimension of Kernel of Z p Z p ²-Linear Codes

A code [Formula Omitted] is called [Formula Omitted]-linear if it is the Gray image of a [Formula Omitted]-additive code. For any prime number [Formula Omitted] larger than 3, the bounds of the rank of [Formula Omitted]-linear codes are given. For each value of the rank and the pairs of rank and the dimension of the kernel of [Formula Omitted]-linear codes, we give detailed construction of the corresponding codes. As an example, the rank and the dimension of the kernel of [Formula Omitted]-linear codes are studied.