scholarly journals Support weight distribution of linear codes

1992 ◽  
Vol 106-107 ◽  
pp. 311-316 ◽  
Author(s):  
Torleiv Kløve
Keyword(s):  
Weight Distribution ◽  
Linear Codes ◽  
Support Weight

Moments of the support weight distribution of linear codes

2011 ◽  
Vol 67 (2) ◽  
pp. 187-196 ◽  
Author(s):  
İbrahim Özen ◽  
Eda Tekin
Keyword(s):  
Weight Distribution ◽  
Linear Codes ◽  
Support Weight

NOTE ON SUPPORT WEIGHT DISTRIBUTION OF LINEAR CODES OVER

2015 ◽  
Vol 91 (2) ◽  
pp. 345-350 ◽  
Author(s):  
JIAN GAO
Keyword(s):  
Weight Distribution ◽  
Linear Code ◽  
Linear Codes ◽  
Dual Code ◽  
Support Weight

AbstractLet $R=\mathbb{F}_{p}+u\mathbb{F}_{p}$, where $u^{2}=u$. A relation between the support weight distribution of a linear code $\mathscr{C}$ of type $p^{2k}$ over $R$ and its dual code $\mathscr{C}^{\bot }$ is established.

ON THE SUPPORT WEIGHT DISTRIBUTION OF LINEAR CODES OVER THE RING

2016 ◽  
Vol 95 (1) ◽  
pp. 157-163 ◽  
Author(s):  
MINJIA SHI ◽  
JIAQI FENG ◽  
JIAN GAO ◽  
ADEL ALAHMADI ◽  
PATRICK SOLÉ
Keyword(s):  
Weight Distribution ◽  
Linear Code ◽  
Linear Codes ◽  
Dual Code ◽  
Support Weight

Let $R=\mathbb{F}_{p}+u\mathbb{F}_{p}+u^{2}\mathbb{F}_{p}+\cdots +u^{d-1}\mathbb{F}_{p}$, where $u^{d}=u$ and $p$ is a prime with $d-1$ dividing $p-1$. A relation between the support weight distribution of a linear code $\mathscr{C}$ of type $p^{dk}$ over $R$ and the dual code $\mathscr{C}^{\bot }$ is established.

Second Support Weight Distribution of Regular LDPC Code Ensembles

2006 ◽  
Author(s):  
Takayuki Itsui ◽  
Kenta Kasai ◽  
Ryoji Ikegaya ◽  
Tomoharu Shibuya ◽  
Kohichi Sakaniwa
Keyword(s):  
Weight Distribution ◽  
Ldpc Code ◽  
Support Weight

scholarly journals Infinite Families of 2-Designs from a Class of Linear Codes Related to Dembowski-Ostrom Functions

2021 ◽  
pp. 1-15
Author(s):  
Rong Wang ◽  
Xiaoni Du ◽  
Cuiling Fan ◽  
Zhihua Niu
Keyword(s):  
Finite Field ◽  
Weight Distribution ◽  
Coding Theory ◽  
Exponential Sums ◽  
Linear Codes ◽  
Cyclic Codes ◽  
Research Interest ◽  
Combinatorial Formula ◽  
Text Design ◽  
Fixed Weight

Due to their important applications to coding theory, cryptography, communications and statistics, combinatorial [Formula: see text]-designs have attracted lots of research interest for decades. The interplay between coding theory and [Formula: see text]-designs started many years ago. It is generally known that [Formula: see text]-designs can be used to derive linear codes over any finite field, and that the supports of all codewords with a fixed weight in a code also may hold a [Formula: see text]-design. In this paper, we first construct a class of linear codes from cyclic codes related to Dembowski-Ostrom functions. By using exponential sums, we then determine the weight distribution of the linear codes. Finally, we obtain infinite families of [Formula: see text]-designs from the supports of all codewords with a fixed weight in these codes. Furthermore, the parameters of [Formula: see text]-designs are calculated explicitly.

scholarly journals New classes of few-weight ternary codes from simplicial complexes

2021 ◽  
Vol 7 (3) ◽  
pp. 4315-4325
Author(s):  
Yang Pan ◽  
◽  
Yan Liu ◽  
Keyword(s):  
Weight Distribution ◽  
Linear Codes ◽  
Minimum Weight ◽  
Simplicial Complexes ◽  
Mathematical Objects ◽  
First Order ◽  
Ternary Codes

<abstract><p>In this article, we describe two classes of few-weight ternary codes, compute their minimum weight and weight distribution from mathematical objects called simplicial complexes. One class of codes described here has the same parameters with the binary first-order Reed-Muller codes. A class of (optimal) minimal linear codes is also obtained in this correspondence.</p></abstract>

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