Computing Efficiently a Parity-Check Matrix for ℤps-Additive Codes

The $\mathbb {Z}_{p^{s}}$ -additive codes of length n are subgroups of $\mathbb {Z}_{p^{s}}^{n}$ , with p prime and $s\geq 1$ . They can be seen as a generalization of linear codes over $\mathbb {Z}_{2}$ , $\mathbb {Z}_{4}$ , or more general over $\mathbb {Z}_{2^{s}}$ . In this paper, we show two methods for computing a parity-check matrix of a $\mathbb {Z}_{p^{s}}$ -additive code from a generator matrix of the code in standard form. We also compare the performance of our results implemented in Magma with the current available function in Magma for linear codes over finite rings in general. Complementing this comparison, we also show a time complexity analysis of the algorithms. The rings $\mathbb {Z}_{p^{s}}$ belong to a more general class of rings: finite chain rings. Along the paper, we observe that the same results can be applied to any linear code over a finite commutative chain ring.