Information on Result #1317956
Linear OA(4109, 137, F4, 57) (dual of [137, 28, 58]-code), using construction X with Varšamov bound based on
- linear OA(4108, 135, F4, 57) (dual of [135, 27, 58]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4107, 133, F4, 57) (dual of [133, 26, 58]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4105, 130, F4, 57) (dual of [130, 25, 58]-code), using
- discarding factors / shortening the dual code based on linear OA(4105, 135, F4, 57) (dual of [135, 30, 58]-code), using
- 2 times truncation [i] based on linear OA(4107, 137, F4, 59) (dual of [137, 30, 60]-code), using
- a “GraX†code from Grassl’s database [i]
- 2 times truncation [i] based on linear OA(4107, 137, F4, 59) (dual of [137, 30, 60]-code), using
- discarding factors / shortening the dual code based on linear OA(4105, 135, F4, 57) (dual of [135, 30, 58]-code), using
- linear OA(4105, 131, F4, 55) (dual of [131, 26, 56]-code), using Gilbert–Varšamov bound and bm = 4105 > Vbs−1(k−1) = 1124 395427 628019 502803 439794 830848 713268 100156 944806 022129 793424 [i]
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(4105, 130, F4, 57) (dual of [130, 25, 58]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4107, 134, F4, 56) (dual of [134, 27, 57]-code), using Gilbert–Varšamov bound and bm = 4107 > Vbs−1(k−1) = 23435 488118 718211 402069 300420 278953 179564 702295 134102 462419 993856 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(4107, 133, F4, 57) (dual of [133, 26, 58]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4108, 136, F4, 56) (dual of [136, 28, 57]-code), using Gilbert–Varšamov bound and bm = 4108 > Vbs−1(k−1) = 66596 223190 721181 792711 377797 502751 380008 155577 463727 157825 933696 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code) (see above)
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
None.