Hamming weight distributions of multi-twisted codes over finite fields

2021 ◽  
Author(s):  
Varsha Chauhan ◽  
Anuradha Sharma ◽  
Sandeep Sharma ◽  
Monika Yadav
Keyword(s):  
Finite Fields ◽  
Hamming Weight ◽  
Weight Distributions

scholarly journals Certain Types of Linear Codes over the Finite Field of Order Twenty-Five

2021 ◽  
pp. 4019-4031
Author(s):  
Emad Bakr Al-Zangana ◽  
Elaf Abdul Satar Shehab
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Weight Distribution ◽  
Incidence Matrix ◽  
Linear Codes ◽  
Projective Line ◽  
Three Dimensions ◽  
Hamming Weight ◽  
Maximum Distance Separable ◽  
Maximum Distance Separable Codes

The aim of the paper is to compute projective maximum distance separable codes, -MDS of two and three dimensions with certain lengths and Hamming weight distribution from the arcs in the projective line and plane over the finite field of order twenty-five. Also, the linear codes generated by an incidence matrix of points and lines of  were studied over different finite fields.  

scholarly journals On the Hyper-Kloosterman Codes Over Galois Rings

2020 ◽  
Vol 12 (2) ◽  
pp. 12
Author(s):  
Etienne TANEDJEU ASSONGMO
Keyword(s):  
Finite Fields ◽  
Linear Code ◽  
Hamming Weight ◽  
Galois Rings

The Hyper-Kloosterman code was first defined over finite fields by Chinen-Hiramatsu, see (Chinen, & Hiramatsu, 2001). In the present paper we define the Hyper-Kloosterman codes over Galois rings R(pe;m). We show that this code is the trace of linear code over R(pe;m). By the Hyper-Kloostermann sums over Galois rings, we determine the Hamming weight of any codeword of this code over Galois rings.

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 Weight Distributions of Regular Low-Density Parity-Check Codes Over Finite Fields

2011 ◽  
Vol 57 (11) ◽  
pp. 7507-7521 ◽  
Author(s):  
Shengtian Yang ◽  
Thomas Honold ◽  
Yan Chen ◽  
Zhaoyang Zhang ◽  
Peiliang Qiu
Keyword(s):  
Finite Fields ◽  
Low Density ◽  
Parity Check ◽  
Low Density Parity Check ◽  
Weight Distributions ◽  
Parity Check Codes

Finite Fields

1996 ◽  
Author(s):  
Rudolf Lidl ◽  
Harald Niederreiter
Keyword(s):  
Finite Fields
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