Optimal Linear Codes Over GF(7) and GF(11) with Dimension 3

Author(s):

M. Emami , L. Pedram

Message:
Abstract:
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.
Keywords:

Linear codes , Optimal codes , Griesmer bound

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:10 Issue: 1, May 2015
Pages:
11 to 22
https://www.magiran.com/p1401953