Database of two-weight codes
This module stores a database of two-weight codes.
\(q=2\) |
\(n=68\) |
\(k=8\) |
\(w_1=32\) |
\(w_2=40\) |
Shared by Eric Chen [ChenDB]. |
\(q=2\) |
\(n=85\) |
\(k=8\) |
\(w_1=40\) |
\(w_2=48\) |
Shared by Eric Chen [ChenDB]. |
\(q=2\) |
\(n=70\) |
\(k=9\) |
\(w_1=32\) |
\(w_2=40\) |
Found by Axel Kohnert [Kohnert07] and shared by Alfred Wassermann. |
\(q=2\) |
\(n=73\) |
\(k=9\) |
\(w_1=32\) |
\(w_2=40\) |
Shared by Eric Chen [ChenDB]. |
\(q=2\) |
\(n=219\) |
\(k=9\) |
\(w_1=96\) |
\(w_2=112\) |
Shared by Eric Chen [ChenDB]. |
\(q=2\) |
\(n=198\) |
\(k=10\) |
\(w_1=96\) |
\(w_2=112\) |
Shared by Eric Chen [ChenDB]. |
\(q=3\) |
\(n=15\) |
\(k=4\) |
\(w_1=9\) |
\(w_2=12\) |
Shared by Eric Chen [ChenDB]. |
\(q=3\) |
\(n=55\) |
\(k=5\) |
\(w_1=36\) |
\(w_2=45\) |
Shared by Eric Chen [ChenDB]. |
\(q=3\) |
\(n=56\) |
\(k=6\) |
\(w_1=36\) |
\(w_2=45\) |
Shared by Eric Chen [ChenDB]. |
\(q=3\) |
\(n=84\) |
\(k=6\) |
\(w_1=54\) |
\(w_2=63\) |
Shared by Eric Chen [ChenDB]. |
\(q=3\) |
\(n=98\) |
\(k=6\) |
\(w_1=63\) |
\(w_2=72\) |
Shared by Eric Chen [ChenDB]. |
\(q=3\) |
\(n=126\) |
\(k=6\) |
\(w_1=81\) |
\(w_2=90\) |
Shared by Eric Chen [ChenDB]. |
\(q=3\) |
\(n=140\) |
\(k=6\) |
\(w_1=90\) |
\(w_2=99\) |
Found by Axel Kohnert [Kohnert07] and shared by Alfred Wassermann. |
\(q=3\) |
\(n=154\) |
\(k=6\) |
\(w_1=99\) |
\(w_2=108\) |
Shared by Eric Chen [ChenDB]. |
\(q=3\) |
\(n=168\) |
\(k=6\) |
\(w_1=108\) |
\(w_2=117\) |
From [Disset00] |
\(q=4\) |
\(n=34\) |
\(k=4\) |
\(w_1=24\) |
\(w_2=28\) |
Shared by Eric Chen [ChenDB]. |
\(q=4\) |
\(n=121\) |
\(k=5\) |
\(w_1=88\) |
\(w_2=96\) |
From [Disset00] |
\(q=4\) |
\(n=132\) |
\(k=5\) |
\(w_1=96\) |
\(w_2=104\) |
From [Disset00] |
\(q=4\) |
\(n=143\) |
\(k=5\) |
\(w_1=104\) |
\(w_2=112\) |
From [Disset00] |
\(q=5\) |
\(n=39\) |
\(k=4\) |
\(w_1=30\) |
\(w_2=35\) |
From Bouyukliev and Simonis ([BS03], Theorem 4.1) |
\(q=5\) |
\(n=52\) |
\(k=4\) |
\(w_1=40\) |
\(w_2=45\) |
Shared by Eric Chen [ChenDB]. |
\(q=5\) |
\(n=65\) |
\(k=4\) |
\(w_1=50\) |
\(w_2=55\) |
Shared by Eric Chen [ChenDB]. |
REFERENCE:
[ChenDB] | (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15) Eric Chen,
Online database of two-weight codes,
http://moodle.tec.hkr.se/~chen/research/2-weight-codes/search.php |
TESTS:
Check the data’s consistency:
sage: from sage.coding.two_weight_db import data
sage: for code in data:
....: M = code['M']
....: assert code['n'] == M.ncols()
....: assert code['k'] == M.nrows()
....: w1,w2 = [w for w,f in enumerate(LinearCode(M).weight_distribution()) if w and f]
....: assert (code['w1'], code['w2']) == (w1, w2)