Module: sage.databases.lincodes
Module-level Functions
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
text, n, k) |
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