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)