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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