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

scholarly journals Weight Distribution of Some Codewords of 3-ary Linear Code over GF(27)‎

2020 ◽  
Vol 31 (4) ◽  
pp. 101
Author(s):  
Maha Majeed Ibrahim ◽  
Emad Bakr Al-Zangana
Keyword(s):  
Weight Distribution ◽  
Linear Code ◽  
Linear Codes ◽  
Generator Matrix ◽  
Weight Distributions

This paper is devoted to introduce the structure of the p-ary linear codes C(n,q) of points and lines of PG(n,q),q=p^h prime. When p=3, the linear code C(2,27) is given with its generator matrix and also, some of weight distributions are calculated.

Some results concerning linear codes and (k, 3)-caps in three-dimensional Galois space

1978 ◽  
Vol 84 (2) ◽  
pp. 191-205 ◽  
Author(s):  
Raymond Hill
Keyword(s):  
Upper Bound ◽  
Coding Theory ◽  
Linear Codes ◽  
Three Dimensional ◽  
Packing Problem ◽  
Error Correcting Codes ◽  
Finite Geometries ◽  
Weight Distributions ◽  
Galois Space

AbstractThe packing problem for (k, 3)-caps is that of finding (m, 3)r, q, the largest size of (k, 3)-cap in the Galois space Sr, q. The problem is tackled by exploiting the interplay of finite geometries with error-correcting codes. An improved general upper bound on (m, 3)3 q and the actual value of (m, 3)3, 4 are obtained. In terms of coding theory, the methods make a useful contribution to the difficult task of establishing the existence or non-existence of linear codes with certain weight distributions.

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 More Constructions of 3-Weight Linear Codes

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lingyong Ma ◽  
Guanjun Li ◽  
Fengyan Liu
Keyword(s):  
Coding Theory ◽  
Exponential Sums ◽  
Linear Codes ◽  
Research Topic ◽  
Plateaued Functions ◽  
Weight Distributions

Linear codes with few weights have become an interesting research topic and important applications of cryptography and coding theory. In this paper, we apply some ternary near-bent and 2-plateaued functions or r -ary functions to construct more 3-weight linear codes, where r is a prime. Moreover, we determine the weight distributions of the resulted linear codes by means of some exponential 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.

Two classes of linear codes and their weight distributions

2017 ◽  
Vol 29 (3) ◽  
pp. 209-225
Author(s):  
Can Xiang ◽  
Xianfang Wang ◽  
Chunming Tang ◽  
Fangwei Fu
Keyword(s):  
Linear Codes ◽  
Weight Distributions
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