29.4 Linear codes

Module: sage.databases.lincodes

Module-level Functions

linear_code_bound( q, n, k, [verbose=False])

Find bounds on the minimum distance of linear codes over GF(q) with length n and dimension k, courtesy of http://www.win.tue.nl/~aeb/voorlincod.html. If no bounds are in the database, returns lower and upper bounds of -1.

INPUT:
    q -- integer, the field order, which must be in
                  [2, 3, 4, 5, 7, 8, 9]
    n -- integer, the length of the code
    k -- integer, the dimension of the code
    verbose -- bool (default=False), print verbose message

OUTPUT:
    integer -- lower bound
    integer -- upper bound
    str -- text about why the bounds are as given

To find lower and upper bounds for values q=7, n=32, k=8, type

sage: lower, upper, text = linear_code_bound(7, 32, 8)     # optional -- needs internet
sage: lower                   # optional 
19
sage: upper                   # optional 
21
sage: text                    # optional 
'Lb(32,8) = 19 DG4\n\nUb(32,8) = 21 follows by a one-step Griesmer bound
from:\nUb(10,7) = 3 is found by considering shortening to:\nUb(9,6) = 3 is
found by construction B:\n[consider deleting the (at most) 6 coordinates of
a word in the dual]'

When bounds are not known the upper and lower returned bounds are -1:

sage: linear_code_bound(9, 32, 200)          # optional -- needs internet
(-1, -1, '(error executing -why-)')

This function raises an IOError if an error occurs downloading data or parsing it. It raises a ValueError if the q input is invalid.

Author: 2005-11-14: Steven Sivek

parse_bound_html( text, n, k)

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