New quantum codes from two linear codes

Abstract

A CSS quantum code is succinctly represented as a pair of linear codes $$(C_1 ,C_2^{\perp })$$ over finite fields $${\mathbb {F}}_{p^e}$$ with $$C_2^{\perp }\subset C_1$$, where p is a prime and e is a positive integer. In this paper, we present two criteria of the $$C_2^{\perp _s}\subset C_1$$ , where $$C_2^{\perp _s}$$ denotes the s-Galois dual of $$C_2$$ and $$0\le s <e$$. Then, using the two criteria, we construct some new quantum codes and a class of new quantum maximum-distance-separable (quantum MDS) codes. In addition, our obtained quantum MDS codes have parameters better than the ones available in the literature.