TY - JOUR
T1 - Optimal Linear Codes Over GF(7) and GF(11) with Dimension 3
TT -
JF - IJMSI
JO - IJMSI
VL - 10
IS - 1
UR - http://ijmsi.ir/article-1-384-en.html
Y1 - 2015
SP - 11
EP - 22
KW - Linear codes
KW - Optimal codes
KW - Griesmer bound.
N2 - Let $n_q(k,d)$ denote the smallest value of $n$ for which there exists a linear $[n,k,d]$-code over the Galois field $GF(q)$. An $[n,k,d]$-code whose length is equal to $n_q(k,d)$ is called {em optimal}. In this paper we present some matrix generators for the family of optimal $[n,3,d]$ codes over $GF(7)$ and $GF(11)$. Most of our given codes in $GF(7)$ are non-isomorphic with the codes presented before. Our given codes in $GF(11)$ are all new.
M3 10.7508/ijmsi.2015.01.002
ER -