… by one via equivalent codes when q > 2. We study some consequences of the relative hull
properties on entanglement-assisted quantum error-correcting codes and prove the existence …

… Using these MDS codes, we give eleven families of EAQECCs with relatively large minimum
distance as follows. Let q = pe with p being an odd prime number and let be an integer with …

… Lemma 2 [5]: Assume that GRSk(a, v, ∞) defined by (2) is the extended GRS code relative
to a and v. For a codeword c = (v1 f (α1), v2 f (α2), ··· ,vq f (αq), fk−1) of GRSk(a, v, ∞), c is …

… of linear codes with hulls of arbitrary or prescribed dimensions from self-orthogonal codes,
we study Galois hulls of linear codes in … • Under certain relatively weak conditions, we give a …

… Further, we also show that the required condition is relatively weak with respect to the
general Galois inner product and specific Euclidean and Hermitian inner products. …

… of quantum computation and quantum communication, how to construct quantum codes to
counteract the noise in quantum … , the dimensions of Galois hulls are also relatively flexible. …

… quantum coding theory. In this paper, we study the hull of generalized Reed-Solomon codes
… [5] Assume that GRSk(a, v, ∞) defined by (2) is the extended GRS code relative to a and v. …

… MDS codes with lower bounded dimension Hermitian hulls … hulls to construct
entanglement-assisted quantum codes. … such that h is relatively large. Then we have at least h …

… When we consider two linear codes instead of one, the idea of relative hull and linear
complementary pairs emerge. The next definition gives such a description. Definition 3: Let C1 and …

… As applications, we explicitly determine the parameters of all MDS entanglement-assisted
quantum error-correcting codes constructed from RS codes; all linear complementary dual (…