Nonexistence of linear codes meeting the Griesmer bound

2022 ◽  
Vol 345 (4) ◽  
pp. 112744
Author(s):  
Wen Ma ◽  
Jinquan Luo
Keyword(s):  
Linear Codes ◽  
Griesmer Bound

scholarly journals On the Minimum Length of Linear Codes over the Field of 9 Elements

10.37236/6394 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Kazuki Kumegawa ◽  
Ysukasa Okazaki ◽  
Tatsuya Maruta
Keyword(s):  
Linear Codes ◽  
Minimum Length ◽  
Griesmer Bound ◽  
Projective Geometries ◽  
Geometric Techniques

We construct a lot of new $[n,4,d]_9$ codes whose lengths are close to the Griesmer bound and prove the nonexistence of some linear codes attaining the Griesmer bound using some geometric techniques through projective geometries to determine the exact value of $n_9(4,d)$ or to improve the known bound on $n_9(4,d)$ for given values of $d$, where $n_q(k,d)$ is the minimum length $n$ for which an $[n,k,d]_q$ code exists. We also give the updated table for $n_9(4,d)$ for all $d$ except some known cases.

On the covering radius of binary, linear codes meeting the Griesmer bound

1985 ◽  
Vol 31 (4) ◽  
pp. 465-468 ◽  
Author(s):  
P. Busschbach ◽  
M. Gerretzen ◽  
H. van Tilborg
Keyword(s):  
Linear Codes ◽  
Covering Radius ◽  
Griesmer Bound ◽  
Binary Linear Codes
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