Bounds on the minimum distance of linear codes

Bounds on linear codes [236,9] over GF(4)

lower bound:161
upper bound:170

Construction

Construction of a linear code [236,9,161] over GF(4):
[1]:  [255, 245, 4] Cyclic Linear Code over GF(2^2)
     CyclicCode of length 255 with generating polynomial x^10 + x^9 + w*x^8 + w^2*x^7 + w^2*x^6 + w*x^2 + w^2*x + w
[2]:  [255, 10, 176] Cyclic Linear Code over GF(2^2)
     Dual of [1]
[3]:  [240, 10, 164] Linear Code over GF(2^2)
     Puncturing of [2] at { 1, 18, 35, 52, 69, 86, 103, 120, 137, 154, 171, 188, 205, 222, 239 }
[4]:  [239, 9, 164] Linear Code over GF(2^2)
     Shortening of [3] at { 240 }
[5]:  [236, 9, 161] Linear Code over GF(2^2)
     Puncturing of [4] at { 237 .. 239 }

last modified: 2008-05-17

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

Lb(236,9) = 161 is found by shortening of:
Lb(237,10) = 161 is found by truncation of:
Lb(240,10) = 164 GW1

Ub(236,9) = 170 is found by considering shortening to:
Ub(235,8) = 170 is found by considering truncation to:
Ub(233,8) = 168 DM4
References
DM4: R. N. Daskalov & E. Metodieva, The Linear Programming Bound for Ternary and Quaternary Linear Codes, preprint, Jan 2002.

GW1: M. Grassl & G. White, New Good Linear Codes by Special Puncturings, ISIT 2004 Chicago USA June 27 - July 2 2004.

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 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


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