Hull linear codes
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 … 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 …
Hull linear codes
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Web28 jan. 2024 · The Euclidean hull dimension of a linear code is an important quantity to determine the parameters of an entanglement-assisted quantum error-correcting … WebThe ℓ-Galois hull hℓ(C) of an [n,k] linear code C over a finite field Fq is the intersection of C and C⊥ℓ, where C⊥ℓ denotes the ℓ-Galois dual of C which intro-duced by Fan and Zhang (2024). The ℓ- Galois LCD code is a linear code C with hℓ(C) = 0. In this paper, we show that the dimension of the ℓ-Galois hull of a
Web6 jul. 2024 · The Galois hull of a linear code is the intersection of itself and its Galois dual code, which has aroused the interest of researchers in these y ears. In this paper, we …
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 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. …
Web1 mrt. 2024 · Recently, the hull dimension of a linear code has been applied to compute some parameters of an entanglementassisted quantum error-correcting code (EAQECC) …
Web19 nov. 1995 · It is clear that Hull (C) is also a linear code. There are many applications of the hull, e.g., determining the complexity of algorithms for checking equivalence of linear codes,... latin name for lavandinWebwe 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. latin name for licorice rootWeb23 feb. 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 … latin name for lightWeb29 jun. 2024 · Our method can be applied to the generalized Reed-Solomon codes and the generalized twisted Reed-Solomon codes to construct arbitrary dimension hull MDS … latin name for ladybugWeb4 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 … latin name for lonelyWebCode1 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] latin name for jaguarWeb8 apr. 2024 · The hull of a linear code over finite fields is the intersection of the code and its dual, which was introduced by Assmus and Key. In this paper, we develop a method to construct linear codes with ... latin name for lions mane