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.

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.

scholarly journals The geometry of Hermitian self-orthogonal codes

2021 ◽  
Vol 113 (1) ◽  
Author(s):  
Simeon Ball ◽  
Ricard Vilar
Keyword(s):  
Linear Code ◽  
Linear Codes ◽  
Generator Matrix ◽  
Hermitian Forms ◽  
Orthogonal Codes ◽  
Orthogonal Code ◽  
Common Zeros

AbstractWe prove that if $$n >k^2$$ n > k 2 then a k-dimensional linear code of length n over $${\mathbb F}_{q^2}$$ F q 2 has a truncation which is linearly equivalent to a Hermitian self-orthogonal linear code. In the contrary case we prove that truncations of linear codes to codes equivalent to Hermitian self-orthogonal linear codes occur when the columns of a generator matrix of the code do not impose independent conditions on the space of Hermitian forms. In the case that there are more than n common zeros to the set of Hermitian forms which are zero on the columns of a generator matrix of the code, the additional zeros give the extension of the code to a code that has a truncation which is equivalent to a Hermitian self-orthogonal code.

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.

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

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>

Characterization of Elution Chromatography Fractions from CIS-Polybutadiene by GPC

1970 ◽  
Vol 43 (6) ◽  
pp. 1439-1450 ◽  
Author(s):  
W. V. Smith ◽  
S. Thiruvengada
Keyword(s):  
Molecular Weight ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Low Molecular Weight ◽  
Molecular Weight Distributions ◽  
Weight Distributions ◽  
Log Normal ◽  
Analytical Fractionation ◽  
Molecular Weight Fractions ◽  
Elution Chromatography

Abstract A preparative fractionation of about 23 g of a commercial cis-polybutadiene rubber is described. The method employed was a solvent elution chromatographic method with very little temperature gradient. The molecular weight distributions of the fractions obtained were determined by an analytical fractionation of 20 mg of polymer. The method was similar to the preparative fractionation and involved solvent elution chromatography. The fractions obtained were assayed for quantity, molecular weight, and molecular weight distribution by GPC. The low molecular weight fractions of the preparative fractionation had molecular weight distributions which could be closely approximated by two log normal distributions, the low molecular weight component having the narrower width. The ratio of weight to number average molecular weight was found to be about 1.1 for these samples. The higher molecular weight fractions could also be approximated by two log normal distributions; however, in these fractions the low molecular weight component had a very broad distribution but constituted only a small portion of the sample. The widths of the GPC curves of the fractions correlate satisfactorily with the molecular weight distributions found by the analytical refractionations. The GPC width is a sensitive criterion of the width of the molecular weight distribution even when only two columns are used. It is felt that the analytical fractionation procedure presented gives more detailed information on the molecular weight distribution than is easily obtainable from an ordinary GPC curve.

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