Hull linear codes
Web9 jan. 2024 · In [], the notion of hulls has been introduced and applied in the characterization of finite projective planes.In [3, 4, 8, 10], it has been shown that the complexity of some algorithms in coding theory can be determined by the hull dimension of codes.Precisely, most of the algorithms work for linear codes with small hull. Due to … WebHull(C) = {0}. Specifically, a linear code C is self-dual if and only if the dimension of Hull(C) is n 2 for even n, where n is the length of C. Hulls of linear codes have been introduced to classify finite projective planes in [1]. Later, it turned out that hulls of linear codes play a vital role in determining the complexity of
Hull linear codes
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Web10 mrt. 2024 · The hull of a linear code was studied by Assmus et al. to classify finite projective planes. In coding theory, the hull of a linear code plays a crucial role in … Web31 mrt. 2024 · The intersection of a linear code and its dual is called the hull of this code. The code is a linear complementary dual (LCD) code if the dimension of its hull is zero. …
Web29 jun. 2024 · In this paper, we develop a method to construct linear codes with trivial hull ( LCD codes) and one-dimensional hull by employing the positive characteristic …
Web4 jan. 2024 · On the opposite direction we prove that a linear LCD code over F 2 s satisfying d ≥ 2 and d ⊥ ≥ 2 is equivalent to a linear one-dimension hull code under a … Web16 jan. 2024 · The Euclidean hull of a linear code has been applied to the so-called entanglement-assisted quantum error-correcting codes (EAQECCs) via classical error …
Web5 jan. 2024 · The hull of linear codes has recently found its application to the so-called entanglement-assisted quantum error-correcting codes (EAQECCs). In this paper, …
Web28 jul. 2024 · Hulls of linear codes have been of interest and extensively studied due to their wide applications. In this paper, we focus on constructions and optimality of linear … screen printing in phoenix azWebwe obtain a necessary and sufficient condition for a linear code to be an -Galois LCD code. In Sect. 4, we first show that the dimension of any -Galois hull of a linear code is invariant under permutation equivalences for 0 ≤ ≤ e − 1. For ternary codes, the dimension of the -Galois hull is also invariant under monomial equivalences. screen printing in raleigh ncWebCode1 Code2 Code3 Code4 Code4 Ternary linear codes with one-dimensional hull Database for the paper ``On the minimum distances of optimal ternary linear codes with one-dimensional hull” Ternary linear codes with one-dimensional hull for $n\leq 20$ n=3 [3, 1, 3] Cyclic Linear Code over GF(3) Generator matrix: [1 1 1] screen printing in spanishWeb6 aug. 2024 · The hull plays an important role in determining the complexity of algorithms for checking permutation equivalence of two linear codes and computing the automorphism … screen printing in primary schoolWeb21 sep. 2024 · The hull of a linear code is defined to be the intersection of the code and its dual. When the size of the hull is small, it has been proved that some algorithms for … screenprinting in shelby ncWeb27 sep. 2024 · The total complexity of this support splitting algorithm is polynomial in the length of the code and exponential in the dimension of the hull of linear codes. A linear … screen printing in seminole flWebThe Euclidean (resp. Hermitian) hull of a linear code C is defined to be Hull E(C) := C\C?(resp. Hull H(C) := C\ C? H). Let h E(C) (resp. h H(C)) be the dimension of Hull … screen printing in portland or