Bounds on the minimum distance of linear codes
Bounds on linear codes [16,4] over GF(8)
ConstructionConstruction type: MPa
Construction of a linear code [16,4,12] over GF(8):
: [16, 4, 12] Linear Code over GF(2^3)
Construction from a stored generator matrix:
[ 1, 0, 0, 0, w, 1, w^4, 1, w^2, w, w^5, w^2, w^3, 0, w^6, w^5 ]
[ 0, 1, 0, 0, 1, w, w^2, w^4, w^3, w, w^4, 1, w^6, w^5, w^3, w^5 ]
[ 0, 0, 1, 0, 1, w^3, w, 0, w^3, w^6, w^5, w^5, w^2, w^6, 1, w^2 ]
[ 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] where w:=Root(x^3 + x + 1)[1,1];
last modified: 2007-07-31
From Brouwer's table (as of 2007-02-13)
Lb(16,4) = 12 MPa
Ub(16,4) = 12 follows by the Griesmer bound.
Stefano Marcugini, Alfredo Milani & Fernanda Pambianco, email 2000-2002.
Idem, Existence and classification of NMDS codes over GF(5) and GF(7),
Seventh International Workshop on Alg. and Combin. Coding Theory, Bansko,
Bulgaria, 18-24 June 2000.
Idem, NMDS Codes of Maximal Length Over F_q, 8<=q<=11, IEEE Transactions
on Informations Theory, 48, No.4, 2002.
- All codes establishing the lower bounds were constructed using
- 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 2001-2006.
- 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 e-mail:
codes [at] codetables.de
New Query |
This page is maintained by
Last change: 30.12.2011