lower bound: | 43 |

upper bound: | 54 |

Construction of a linear code [106,23,43] over GF(3): [1]: [1, 1, 1] Cyclic Linear Code over GF(3) RepetitionCode of length 1 [2]: [104, 22, 42] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 104 with generating polynomials: 2*x^50 + x^49 + x^48 + 2*x^46 + x^45 + x^44 + x^43 + x^42 + 2*x^41 + 2*x^40 + 2*x^38 + 2*x^34 + 2*x^33 + x^30 + 2*x^28 + 2*x^25 + 2*x^23 + x^22 + x^21 + x^14, 2*x^51 + 2*x^50 + x^49 + 2*x^48 + x^47 + x^45 + 2*x^44 + 2*x^38 + 2*x^37 + x^36 + 2*x^32 + 2*x^31 + 2*x^30 + x^27 + 2*x^26 + 2*x^25 + 2*x^24 + 2*x^23 + x^22 + 2*x^20 + 2*x^19 + 2*x^17 + 2*x^16 + 2*x^15 + x^13 + 2*x^12 + x^11 + 2*x^10 + x^9 + 2*x^8 + x^5 + 2*x [3]: [104, 22, 42] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 104 with generating polynomials: 2*x^51 + x^50 + x^49 + x^46 + x^42 + x^41 + 2*x^40 + x^39 + 2*x^38 + 2*x^37 + x^34 + 2*x^31 + x^30 + x^29 + x^27 + 2*x^26 + 2*x^25 + 2*x^24 + x^23 + x^10, 2*x^51 + x^50 + 2*x^49 + 2*x^48 + x^43 + x^42 + 2*x^41 + x^40 + 2*x^39 + 2*x^38 + x^37 + x^36 + 2*x^34 + x^32 + 2*x^31 + 2*x^30 + x^29 + 2*x^26 + x^25 + x^23 + x^19 + x^17 + x^15 + x^14 + x^13 + x^11 + x^10 + 2*x^8 + x^7 + x^5 + x^3 + x^2 [4]: [104, 23, 41] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 104 with generating polynomials: x^51 + 2*x^50 + x^49 + x^48 + 2*x^47 + 2*x^45 + x^40 + x^37 + 2*x^36 + x^35 + 2*x^34 + 2*x^32 + x^31 + 2*x^30 + 2*x^29 + 2*x^27 + 2*x^26 + 2*x^25 + 2*x^24 + x^23 + 2*x^22 + x^2, x^51 + x^48 + x^47 + 2*x^46 + 2*x^44 + x^42 + 2*x^40 + x^39 + x^37 + 2*x^35 + x^34 + 2*x^33 + x^30 + 2*x^29 + x^27 + x^25 + 2*x^24 + x^23 + x^22 + x^21 + 2*x^20 + x^19 + 2*x^18 + x^17 + 2*x^16 + x^15 + 2*x^14 + x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^7 + 2*x^6 + 2*x^5 + 2*x^2 + 2*x [5]: [106, 23, 43] Linear Code over GF(3) ConstructionXX using [4] [3] [2] [1] and [1] last modified: 2021-08-26

Lb(106,23) = 41 is found by lengthening of: Lb(105,23) = 41 DaH Ub(106,23) = 54 is found by considering shortening to: Ub(99,16) = 54 Da

** DaH: **
Rumen Daskalov & Plamen Hristov, *New One-Generator Quasi-Cyclic Codes over
GF(7)*, preprint, Oct 2001. R. Daskalov & P Hristov, *New One-Generator
Quasi-Twisted Codes over GF(5), (preprint) Oct. 2001. R. Daskalov & P Hristov,
New Quasi-Twisted Degenerate Ternary Linear Codes, preprint, Nov 2001.
Email, 2002-2003.
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- 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

This page is maintained by Markus Grassl (codes@codetables.de). Last change: 30.12.2011