New quantum codes from self-orthogonal cyclic codes over Fq2[u]/⟨uk⟩

Abstract

In this paper, we propose a construction of q-ary quantum codes from Hermitian self-orthogonal cyclic codes over the finite chain ring R=Fq2[u]/⟨uk⟩, with uk= 0 , where Fq2 is a finite field with q2 elements, q= pm, p a prime. A Gray map from R to Fq2k is defined. Some characterizations of cyclic codes over R have been given in terms of their different types of generators. The structure of their dual codes has also been determined, and a necessary and sufficient condition for these codes to be self-orthogonal is presented. The construction of quantum codes is derived by applying Hermitian construction to the Gray images of self-orthogonal cyclic codes over R. From this construction, we have been able to obtain some new quantum codes with better parameters than some presently known comparable best codes available in the literature. Some of these codes have been given as examples, and the others have been given in the form of two tables. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.