Some Divisible Quaternary Linear Codes
In this page, we give some results on linear codes over the field of order 4
obtained by the exhaustive computer search
using the package Q-Extension.
An m-divisible [n,k,d]_q code means a linear code of length n, dimension k and
minimum weight d over the field of order q.
In tables, "E" and "N" stand for Existence and Nonexistence, respectively.
4-divisible [n,k,4]_4 codes for n ≤ 22 and k=5,6,7,8
| n / k |
5 |
6 |
7 |
8 |
| 1-13 |
N |
N |
N |
N |
| 14 |
E |
N |
N |
N |
| 15 |
E |
E |
N |
N |
| 16 |
E |
N |
N |
N |
| 17 |
E |
N |
N |
N |
| 18 |
E |
E |
N |
N |
| 19 |
E |
E |
E |
N |
| 20 |
E |
E |
E |
E |
| 21 |
E |
E |
E |
N |
| 22 |
E |
E |
E |
N |
4-divisible [n,k,8]_4 codes for n ≤ 22 and k=5,6,7,8
| n / k |
5 |
6 |
7 |
8 |
| 1-15 |
N |
N |
N |
N |
| 16 |
E |
N |
N |
N |
| 17 |
N |
N |
N |
N |
| 18 |
N |
N |
N |
N |
| 19 |
E |
N |
N |
N |
| 20 |
E |
E |
N |
N |
| 21 |
E |
N |
N |
N |
| 22 |
E |
E |
N |
N |
8-divisible [n,k,8]_4 codes for n ≤ 34 and k=5,6,7
| n / k |
5 |
6 |
7 |
| 1-27 |
N |
N |
N |
| 28 |
E |
N |
N |
| 29 |
N |
N |
N |
| 30 |
E |
E |
N |
| 31 |
E |
N |
N |
| 32 |
E |
N |
N |
| 33 |
N |
N |
N |
| 34 |
E |
N |
N |
8-divisible [n,k,16]_4 codes for n ≤ 34 and k=5,6,7
| n / k |
5 |
6 |
7 |
| 1-30 |
N |
N |
N |
| 31 |
E |
N |
N |
| 32 |
E |
E |
N |
| 33 |
N |
N |
N |
| 34 |
N |
N |
N |
See
Some Ternary Divisible Codes
for some 9-divisible ternary linear codes.
See also
Database with linear codes
for dimension k < 7 and
Divisible Linear Codes
.
This page is maintained by
Tatsuya Maruta
.