Results 11 to 20 of about 4,907,516 (322)
Twisted Reed-Solomon Codes [PDF]
International Symposium on Information Theory, 2017 We present a new general construction of MDS codes over a finite field $\mathbb{F}_q$. We describe two explicit subclasses which contain new MDS codes of length at least $q/2$ for all values of $q \ge 11$. Moreover, we show that most of the new codes are
Beelen, Peter +2 more
core +4 more sources
On the Hull-Variation Problem of Equivalent Linear Codes [PDF]
IEEE Transactions on Information Theory, 2022 The intersection ${\mathbf{C}}\bigcap {\mathbf{C}}^{\perp }$ ( ${\mathbf{C}}\bigcap {\mathbf{C}}^{\perp _{h}}$ ) of a linear code ${\mathbf{C}}$ and its Euclidean dual ${\mathbf{C}}^{\perp }$ (Hermitian dual ${\mathbf{C}}^{\perp _{h}}$ ) is called
Haoyuan Chen
semanticscholar +1 more source
FeynCalc 10: Do multiloop integrals dream of computer codes? [PDF]
Computer Physics Communications, 2023 In this work we report on a new version of FeynCalc, a Mathematica package widely used in the particle physics community for manipulating quantum field theoretical expressions and calculating Feynman diagrams.
Vladyslav Shtabovenko +2 more
semanticscholar +1 more source
Blocking sets, minimal codes and trifferent codes [PDF]
Journal of the London Mathematical Society, 2023 We prove new upper bounds on the smallest size of affine blocking sets, that is, sets of points in a finite affine space that intersect every affine subspace of a fixed codimension.
Anurag Bishnoi +3 more
semanticscholar +1 more source
Linear Codes Over 𝔽q Are Equivalent to LCD Codes for q>3 [PDF]
IEEE Transactions on Information Theory, 2018 The hull H ( C ) of a linear code C is defined by H ( C ) = C ∩ C ⊥ . A linear code with a complementary dual (LCD) is a linear code with H ( C ) = { 0 } . The dimension of the hull of a code is an invariant under permutation equivalence.
C. Carlet +4 more
semanticscholar +2 more sources
Generic Reed-Solomon Codes Achieve List-Decoding Capacity [PDF]
Symposium on the Theory of Computing, 2022 In a recent paper, Brakensiek, Gopi and Makam introduced higher order MDS codes as a generalization of MDS codes. An order-ℓ MDS code, denoted by MDS(ℓ), has the property that any ℓ subspaces formed from columns of its generator matrix intersect as ...
Joshua Brakensiek, S. Gopi, V. Makam
semanticscholar +1 more source
Many Non-Reed-Solomon Type MDS Codes From Arbitrary Genus Algebraic Curves [PDF]
IEEE Transactions on Information Theory, 2022 It is always interesting and important to construct non-Reed-Solomon type MDS codes in coding theory and finite geometries. In this paper, we prove that many non-Reed-Solomon type MDS codes from arbitrary genus algebraic curves can be constructed.
Hao Chen
semanticscholar +1 more source
Relative Hulls and Quantum Codes [PDF]
IEEE Transactions on Information Theory, 2022 Given two $q$ -ary codes $C_{1}$ and $C_{2}$ , the relative hull of $C_{1}$ with respect to $C_{2}$ is the intersection $C_{1}\cap C_{2}^{\perp} $ .
S. Anderson +5 more
semanticscholar +1 more source
New LCD MDS Codes of Non-Reed-Solomon Type [PDF]
IEEE Transactions on Information Theory, 2021 Both linear complementary dual (LCD) codes and maximum distance separable (MDS) codes have good algebraic structures, and they have interesting practical applications such as communication systems, data storage, quantum codes, and so on.
Yansheng Wu, J. Hyun, Yoonjin Lee
semanticscholar +1 more source
On Hard and Soft Decision Decoding of BCH Codes [PDF]
IEEE Transactions on Information Theory, 2021 The binary primitive BCH codes are cyclic and are constructed by choosing a subset of the cyclotomic cosets. Which subset is chosen determines the dimension, the minimum distance and the weight distribution of the BCH code.
M. Bossert +2 more
semanticscholar +1 more source