scholarly journals Twisted Hermitian Codes

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 40
Author(s):  
Austin Allen ◽  
Keller Blackwell ◽  
Olivia Fiol ◽  
Rutuja Kshirsagar ◽  
Bethany Matsick ◽  
...  
Keyword(s):  
Linear Code ◽  
High Dimensional ◽  
Hermitian Codes ◽  
Reed Solomon Codes ◽  
New Codes

We define a family of codes called twisted Hermitian codes, which are based on Hermitian codes and inspired by the twisted Reed–Solomon codes described by Beelen, Puchinger, and Nielsen. We demonstrate that these new codes can have high-dimensional Schur squares, and we identify a subfamily of twisted Hermitian codes that achieves a Schur square dimension close to that of a random linear code. Twisted Hermitian codes allow one to work over smaller alphabets than those based on Reed–Solomon codes of similar lengths.

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].

On the ℤq-Simplex codes and its weight distribution for dimension 2

2015 ◽  
Vol 07 (03) ◽  
pp. 1550030
Author(s):  
C. Durairajan ◽  
J. Mahalakshmi ◽  
P. Chella Pandian
Keyword(s):  
Weight Distribution ◽  
Linear Code ◽  
Prime Power ◽  
Dimension 2 ◽  
New Codes ◽  
Simplex Codes ◽  
Order Element

In this paper, we have defined ℤq-linear code and constructed some new codes. In particular, we have introduced the concept of ℤq-Simplex codes and proved that it is a [Formula: see text]-linear code for any integer q ≥ 2 and k ≥ 3 where p is the least order element in ℤq. We have given the weight distribution of ℤq-Simplex codes of dimension 2 when q is a prime power and when q is a product of distinct primes.

Hermitian codes as generalized Reed-Solomon codes

1992 ◽  
Vol 2 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Tomik Yaghoobian ◽  
Ian F. Blake
Keyword(s):  
Hermitian Codes ◽  
Reed Solomon Codes
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