In this paper we characterize the algebraic structure of two-dimensional \((\alpha ,\beta )\)-constacyclic codes of arbitrary length \(s\ell \) and of their duals over a finite field \(\mathbb{F}_q \), where \(\alpha ,\beta\) are non zero elements of \(\mathbb{F}_q \). For \(\alpha ,\beta \in \{1,-1\}\), we give necessary and sufficient conditions for a two-dimensional \((\alpha ,\beta )\)-constacyclic code to be self-dual. We also show that a two-dimensional \((\alpha ,1 )\)-constacyclic code \({\mathcal {C}}\) of length \(n=s\ell \) cannot be self-dual if \(\gcd (s,q)= 1\). Finally, we give some examples of self-dual, isodual, MDS and quasi-twisted codes corresponding to two-dimensional \((\alpha ,\beta )\)-constacyclic codes.

在本文中，我们描述了二维\((\alpha ,\beta )\) - 任意长度\(s\ell \)和它们在有限域\(\mathbb{F }_q \)，其中\(\alpha ,\beta\)是\(\mathbb{F}_q \) 的非零元素。对于\(\alpha ,\beta \in \{1,-1\}\)，我们给出了二维\((\alpha ,\beta )\) -constacyclic code 的充分必要条件双。我们还表明，长度为\(n=s\ell \)的二维\((\alpha ,1 )\) -constacyclic code \({\mathcal {C}}\)不能是自对偶的，如果\(\gcd (s,q)= 1\)。最后，我们给出了与二维\((\alpha,\beta)\)- constacyclic 码对应的自对偶、等向、MDS 和准扭曲码的一些例子。