scholarly journals A formula on the weight distribution of linear codes with applications to AMDS codes

2022 ◽  
Vol 77 ◽  
pp. 101933
Author(s):  
Alessio Meneghetti ◽  
Marco Pellegrini ◽  
Massimiliano Sala
Keyword(s):  
Weight Distribution ◽  
Linear Codes ◽  
Amds Codes

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>

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

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 Weight Distribution of Periodic Errors and Optimal/Anti-Optimal Linear Codes

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Pankaj Kumar Das
Keyword(s):  
Weight Distribution ◽  
Linear Codes ◽  
Parity Check ◽  
Optimal Linear ◽  
Optimal Linear Codes

The paper discusses weight distribution of periodic errors and then the optimal case on bounds of parity check digits for (n=n1+n2,k) linear codes overGF(q)that corrects all periodic errors of orderrin the first block of lengthn1and all periodic errors of ordersin the second block of lengthn2and no others. Further, we extend the study to the case when the errors are in the form of periodic errors of orderr(ands) or more in the two subblocks.

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