Hull linear codes
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
Hull linear codes
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Web27 okt. 2024 · Linear codes with good parameters have wide applications in secret sharing schemes, authentication codes, association schemes, consumer electronics and communications, etc. During the past four decades, constructions of linear codes with good parameters received much attention and many classes of such codes were presented. … 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. …
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 … Web6 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 …
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,... 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 …
Web16 mrt. 2024 · The hull determines the complexity of algorithms for checking permutation equivalence of two linear codes (Sendrier 2000), which are very effective if the …
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) … monckeberg medial calcificationWeb16 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 … monckeberg atherosclerosisWeb24 okt. 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 trivial hull (LCD codes) and one-dimensional hull by … monchy\u0027s restaurant rahway njWebCode1 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] moncks corner ame church facebook liveWeb9 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 … ibm tampa officeWeb29 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 … ibm tape drive commandsWeb21 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 … ibm tape encryption