Bounds on the minimum distance of linear codes
Bounds on linear codes [75,11] over GF(5)
lower bound:  45 
upper bound:  52 
Construction
Construction type: EricChen
Construction of a linear
code [75,11,45] over GF(5):
[1]: [75, 11, 45] Quasicyclic of degree 5 Linear Code over GF(5)
QuasiCyclicCode of length 75 with generating polynomials: 3*x^14 + 3*x^13 +
4*x^12 + x^11 + x^4, 2*x^14 + 3*x^11 + 3*x^9 + 2*x^8 + 3*x^7 + 3*x^4 + 3*x^3 +
2*x^2 + 3*x + 3, 2*x^14 + 2*x^12 + 3*x^11 + 4*x^10 + 4*x^9 + 2*x^8 + 3*x^7 +
3*x^6 + 2*x^4 + 3*x^3 + 3*x, 2*x^14 + 3*x^13 + x^12 + 3*x^11 + x^8 + 4*x^5 +
2*x^3 + 2*x^2 + 4*x + 4, 2*x^14 + 2*x^13 + 2*x^11 + 3*x^10 + x^7 + 2*x^5 +
2*x^4 + x^3 + 4*x^2 + 2*x + 4
last modified: 20210825
From Brouwer's table (as of 20070213)
Lb(75,11) = 44 is found by shortening of:
Lb(76,12) = 44 is found by truncation of:
Lb(78,12) = 46 DaH
Ub(75,11) = 52 follows by a onestep Griesmer bound from:
Ub(22,10) = 10 follows by a onestep Griesmer bound from:
Ub(11,9) = 2 is found by considering shortening to:
Ub(7,5) = 2 is found by construction B:
[consider deleting the (at most) 5 coordinates of a word in the dual]
References
DaH:
Rumen Daskalov & Plamen Hristov, New OneGenerator QuasiCyclic Codes over
GF(7), preprint, Oct 2001. R. Daskalov & P Hristov, New OneGenerator
QuasiTwisted Codes over GF(5), (preprint) Oct. 2001. R. Daskalov & P Hristov,
New QuasiTwisted Degenerate Ternary Linear Codes, preprint, Nov 2001.
Email, 20022003.
Notes
 All codes establishing the lower bounds were constructed using
MAGMA.
 Upper bounds are taken from the tables of Andries E. Brouwer, with the exception of codes over GF(7) with n>50.
For most of these codes, the upper bounds are rather weak.
Upper bounds for codes over GF(7) with small dimension have been provided by Rumen Daskalov.
 Special thanks to John Cannon for his support in this project.
 A prototype version of MAGMA's code database over GF(2) was
written by Tat Chan in 1999 and extended later that year by
Damien Fisher. The current release version was
developed by Greg White over the period 20012006.
 Thanks also to Allan Steel for his MAGMA support.
 My apologies to all authors that have contributed codes to this table for not giving specific credits.
 If you have found any code improving the bounds or some errors, please send me an email:
codes [at] codetables.de

Homepage 
New Query 
Contact
This page is maintained by
Markus Grassl
(grassl@ira.uka.de).
Last change: 30.12.2011