Bounds on the minimum distance of linear codes

Bounds on linear codes [252,16] over GF(2)

lower bound:112
upper bound:118


Construction of a linear code [252,16,112] over 
[1]:  [256, 21, 112] Linear Code over GF(2)
     Extended BCHCode with parameters 255 111
[2]:  [252, 17, 112] Linear Code over GF(2)
     Shortening of [1] at { 253 .. 256 }
[3]:  [252, 16, 112] Linear Code over GF(2)
     Subcode of [2]

last modified: 2001-01-30

From Brouwer's table (as of 2007-02-13)

Lb(252,16) = 112 is found by taking a subcode of:
Lb(252,17) = 112 is found by shortening of:
Lb(256,21) = 112 XBC

Ub(252,16) = 118 follows by a one-step Griesmer bound from:
Ub(133,15) = 59 is found by considering shortening to:
Ub(132,14) = 59 Ja 
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996,

XBC: Extended BCH code.


  • 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 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]

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