Database of two-weight codesΒΆ

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:

[BS03]I. Bouyukliev and J. Simonis, Some new results on optimal codes over \(F_5\), Designs, Codes and Cryptography 30, no. 1 (2003): 97-111, http://www.moi.math.bas.bg/moiuser/~iliya/pdf_site/gf5srev.pdf,
[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
[Kohnert07](1, 2) A. Kohnert, Constructing two-weight codes with prescribed groups of automorphisms, Discrete applied mathematics 155, no. 11 (2007): 1451-1457. http://linearcodes.uni-bayreuth.de/twoweight/
[Disset00](1, 2, 3, 4) L. Dissett, Combinatorial and computational aspects of finite geometries, 2000, https://tspace.library.utoronto.ca/bitstream/1807/14575/1/NQ49844.pdf

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)