lower bound: | 26 |

upper bound: | 32 |

Construction of a linear code [99,31,26] over GF(2): [1]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [2]: [96, 29, 26] Quasicyclic of degree 3 Linear Code over GF(2) QuasiCyclicCode of length 96 with generating polynomials: x^31 + x^30 + x^29 + x^24, x^31 + x^30 + x^26 + x^24 + x^20 + x^17 + x^14 + x^11 + x^10 + x^9 + x^7 + x^6 + x^5 + x^4, x^31 + x^29 + x^27 + x^25 + x^24 + x^21 + x^19 + x^14 + x^13 + x^12 + x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + x + 1 [3]: [96, 31, 24] Quasicyclic of degree 3 Linear Code over GF(2) QuasiCyclicCode of length 96 stacked to height 2 with generating polynomials: 0, x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^30 + 1, x^31 + x^28 + x^26 + x^25 + x^24 + x^23 + x^21 + x^20 + x^18 + x^16 + x^12 + x^11 + x^9 + x^8 + x^7 + x^3, x^31 + x^27 + x^26 + x^24 + x^20 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^8 + x^6 + x^4 + x^2 + 1 [4]: [99, 31, 26] Linear Code over GF(2) ConstructionX using [3] [2] and [1] last modified: 2021-08-26

Lb(99,31) = 25 DaH Ub(99,31) = 32 is found by considering shortening to: Ub(96,28) = 32 otherwise adding a parity check bit would contradict: Ub(97,28) = 33 Bro

** 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:

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