Information on Result #1323880
Linear OA(3242, 6644, F3, 41) (dual of [6644, 6402, 42]-code), using construction X with Varšamov bound based on
- linear OA(3240, 6640, F3, 41) (dual of [6640, 6400, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(30) [i] based on
- linear OA(3217, 6561, F3, 41) (dual of [6561, 6344, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(323, 79, F3, 9) (dual of [79, 56, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(323, 82, F3, 9) (dual of [82, 59, 10]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(323, 82, F3, 9) (dual of [82, 59, 10]-code), using
- construction X applied to Ce(40) ⊂ Ce(30) [i] based on
- linear OA(3240, 6642, F3, 40) (dual of [6642, 6402, 41]-code), using Gilbert–Varšamov bound and bm = 3240 > Vbs−1(k−1) = 2 821126 306943 998562 425855 832184 150021 675520 147733 841454 224730 354427 592721 082826 374356 418864 891677 434848 897795 326531 [i]
- linear OA(30, 2, F3, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3242, 6644, F3, 2, 41) (dual of [(6644, 2), 13046, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3242, 6644, F3, 3, 41) (dual of [(6644, 3), 19690, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(3242, 6644, F3, 4, 41) (dual of [(6644, 4), 26334, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(3242, 6644, F3, 5, 41) (dual of [(6644, 5), 32978, 42]-NRT-code) | [i] | ||
| 5 | Digital (201, 242, 6644)-net over F3 | [i] | ||
| 6 | Linear OOA(3242, 3322, F3, 2, 41) (dual of [(3322, 2), 6402, 42]-NRT-code) | [i] | OOA Folding | |