lower bound: | 89 |

upper bound: | 102 |

Construction of a linear code [176,18,89] over GF(3): [1]: [176, 18, 89] Quasicyclic of degree 2 Linear Code over GF(3) QuasiCyclicCode of length 176 with generating polynomials: x^85 + 2*x^84 + x^83 + 2*x^82 + x^81 + x^80 + x^78 + 2*x^77 + x^76 + x^75 + 2*x^72 + x^71 + x^69 + x^66 + 2*x^64 + 2*x^62 + x^60 + 2*x^59 + x^56 + 2*x^55 + 2*x^52 + x^51 + x^50 + x^48 + 2*x^47 + x^46 + 2*x^43 + x^42 + 2*x^39 + 2*x^38 + 2*x^37 + 2*x^36 + 2*x^32 + 2*x^31 + 2*x^30 + x^29 + 2*x^28 + 2*x^27 + x^26 + x^25 + x^24 + 2*x^22 + 2*x^21 + 2*x^20 + x^19 + x^15, x^87 + 2*x^85 + 2*x^82 + 2*x^81 + 2*x^80 + x^77 + x^76 + x^75 + 2*x^74 + 2*x^72 + 2*x^71 + x^70 + x^69 + x^68 + 2*x^67 + x^66 + 2*x^65 + x^64 + x^63 + x^61 + 2*x^60 + 2*x^59 + 2*x^57 + x^55 + x^53 + x^52 + x^50 + x^49 + x^47 + x^46 + x^42 + 2*x^41 + x^39 + x^38 + 2*x^37 + x^36 + x^34 + x^32 + 2*x^31 + 2*x^29 + x^26 + x^25 + x^23 + x^22 + 2*x^21 + x^16 + 2*x^15 + x^13 + x^12 + 2*x^10 + 2*x^9 + x^8 + 2*x^7 + x^6 + x^5 + 2*x^4 + x^3 + 2 last modified: 2021-08-25

Lb(176,18) = 87 is found by taking a subcode of: Lb(176,19) = 87 DaH Ub(176,18) = 102 is found by considering shortening to: Ub(175,17) = 102 Da2

** 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 (grassl@ira.uka.de). Last change: 30.12.2011