Weight distributions of binary linear codes based on Hadamard matrices

2002 ◽  
Author(s):  
T. Beth ◽  
H. Kalouti ◽  
D.E. Lazic
Keyword(s):  
Linear Codes ◽  
Hadamard Matrices ◽  
Binary Linear Codes ◽  
Weight Distributions

New extremal Type II ℤ4-codes of length 32 obtained from Hadamard matrices

2019 ◽  
Vol 11 (05) ◽  
pp. 1950057
Author(s):  
Sara Ban ◽  
Dean Crnković ◽  
Matteo Mravić ◽  
Sanja Rukavina
Keyword(s):  
Incidence Matrix ◽  
Linear Codes ◽  
Minimum Weight ◽  
Hadamard Matrices ◽  
Binary Codes ◽  
Type Ii ◽  
Hadamard Design ◽  
Binary Linear Codes ◽  
Type Formula ◽  
Hadamard Designs

For every Hadamard design with parameters [Formula: see text]-[Formula: see text] having a skew-symmetric incidence matrix we give a construction of 54 Hadamard designs with parameters [Formula: see text]-[Formula: see text]. Moreover, for the case [Formula: see text] we construct doubly-even self-orthogonal binary linear codes from the corresponding Hadamard matrices of order 32. From these binary codes we construct five new extremal Type II [Formula: see text]-codes of length 32. The constructed codes are the first examples of extremal Type II [Formula: see text]-codes of length 32 and type [Formula: see text], [Formula: see text], whose residue codes have minimum weight 8. Further, correcting the results from the literature we construct 5147 extremal Type II [Formula: see text]-codes of length 32 and type [Formula: see text].

scholarly journals Weight distributions for projective binary linear codes from Weil sums

2021 ◽  
Vol 6 (8) ◽  
pp. 8600-8610
Author(s):  
Shudi Yang ◽  
◽  
Zheng-An Yao ◽  
Keyword(s):  
Linear Codes ◽  
Binary Linear Codes ◽  
Weight Distributions ◽  
Weil Sums

scholarly journals On the most Weight $w$ Vectors in a Dimension $k$ Binary Code

10.37236/414 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Joshua Brown Kramer
Keyword(s):  
Coding Theory ◽  
Binary Code ◽  
Linear Codes ◽  
Complete Solution ◽  
Dimensional Subspace ◽  
Hamming Weight ◽  
Binary Linear Codes ◽  
Linear Map ◽  
Weight Distributions

Ahlswede, Aydinian, and Khachatrian posed the following problem: what is the maximum number of Hamming weight $w$ vectors in a $k$-dimensional subspace of $\mathbb{F}_2^n$? The answer to this question could be relevant to coding theory, since it sheds light on the weight distributions of binary linear codes. We give some partial results. We also provide a conjecture for the complete solution when $w$ is odd as well as for the case $k \geq 2w$ and $w$ even. One tool used to study this problem is a linear map that decreases the weight of nonzero vectors by a constant. We characterize such maps.

scholarly journals Simple Tight Performance Bound Based on the GFBT for Binary Linear Codes

2020 ◽  
Vol 428 ◽  
pp. 012028
Author(s):  
Jia Liu ◽  
Mingyu Zhang ◽  
Rongjun Chen ◽  
Chaoyong Wang ◽  
Xiaofeng An ◽  
...  
Keyword(s):  
Linear Codes ◽  
Performance Bound ◽  
Binary Linear Codes

New binary linear codes which are dual transforms of good codes

1999 ◽  
Vol 45 (6) ◽  
pp. 2136-2137 ◽  
Author(s):  
D.B. Jaffe ◽  
J. Simonis
Keyword(s):  
Linear Codes ◽  
Binary Linear Codes

Several classes of linear codes and their weight distributions

2018 ◽  
Vol 30 (1) ◽  
pp. 75-92 ◽  
Author(s):  
Xiaoqiang Wang ◽  
Dabin Zheng ◽  
Hongwei Liu
Keyword(s):  
Linear Codes ◽  
Weight Distributions
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