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.

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.

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

scholarly journals DUAL CODE AND MACWILLIAMS IDENTITY ON ADDITIVE CODE

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
Miftah Yuliati ◽  
Sri Wahyuni ◽  
Indah Emilia Wijayanti
Keyword(s):  
Weight Distribution ◽  
Linear Code ◽  
Hamming Distance ◽  
Finite Abelian Group ◽  
Dual Code ◽  
Inner Product ◽  
Dual Codes ◽  
Macwilliams Identity ◽  
Homogeneous Weight ◽  
Distance Hamming

Additive code is a generalization of linear code. It is defined as subgroup of a finite Abelian group. The definitions of Hamming distance, Hamming weight, weight distribution, and homogeneous weight distribution in additive code are similar with the definitions in linear code. Different with linear code where the dual code is defined using inner product, additive code using theories in group to define its dual code because in group theory we do not have term of inner product. So, by this thesis, the definitions of dual code in additive code will be discussed. Then, this thesis discuss about a familiar theorem in dual code theory, that is MacWilliams Identity. Next, this thesis discuss about how to proof of MacWilliams Identity on adiitive code using dual codes which are defined.

On some punctured codes of ℤq-Simplex codes

2021 ◽  
pp. 2250012
Author(s):  
J. Prabu ◽  
J. Mahalakshmi ◽  
C. Durairajan ◽  
S. Santhakumar
Keyword(s):  
Prime Divisor ◽  
Weight Distribution ◽  
Linear Code ◽  
Prime Power ◽  
Punctured Codes ◽  
New Codes ◽  
Simplex Codes ◽  
Simplex Code ◽  
Partial Weight ◽  
Unit Formula

In this paper, we have constructed some new codes from [Formula: see text]-Simplex code called unit [Formula: see text]-Simplex code. In particular, we find the parameters of these codes and have proved that it is a [Formula: see text] [Formula: see text]-linear code, where [Formula: see text] and [Formula: see text] is a smallest prime divisor of [Formula: see text]. When rank [Formula: see text] and [Formula: see text] is a prime power, we have given the weight distribution of unit [Formula: see text]-Simplex code. For the rank [Formula: see text] we obtain the partial weight distribution of unit [Formula: see text]-Simplex code when [Formula: see text] is a prime power. Further, we derive the weight distribution of unit [Formula: see text]-Simplex code for the rank [Formula: see text] [Formula: see text].

scholarly journals Nonexistence Proofs for Five Ternary Linear Codes

2002 ◽  
Vol 1 (1) ◽  
pp. 35
Author(s):  
S. GURITMAN
Keyword(s):  
Linear Code ◽  
Minimum Distance ◽  
Linear Codes ◽  
Ternary Linear Codes

<p>An [n,k, dh-code is a ternary linear code with length n, dimension k and minimum distance d. We prove that codes with parameters [110,6, 72h, [109,6,71h, [237,6,157b, [69,7,43h, and [120,9,75h do not exist.</p>

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