Information on Result #1304934
Linear OA(3157, 799, F3, 38) (dual of [799, 642, 39]-code), using 50 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 1, 5 times 0, 1, 8 times 0, 1, 12 times 0, 1, 15 times 0) based on linear OA(3149, 741, F3, 38) (dual of [741, 592, 39]-code), using
- construction XX applied to C1 = C([328,364]), C2 = C([330,365]), C3 = C1 + C2 = C([330,364]), and C∩ = C1 ∩ C2 = C([328,365]) [i] based on
- linear OA(3142, 728, F3, 37) (dual of [728, 586, 38]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {328,329,…,364}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3142, 728, F3, 36) (dual of [728, 586, 37]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {330,331,…,365}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3148, 728, F3, 38) (dual of [728, 580, 39]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {328,329,…,365}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(3136, 728, F3, 35) (dual of [728, 592, 36]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {330,331,…,364}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(30, 6, F3, 0) (dual of [6, 6, 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(3157, 799, F3, 2, 38) (dual of [(799, 2), 1441, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3157, 799, F3, 3, 38) (dual of [(799, 3), 2240, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(3157, 799, F3, 4, 38) (dual of [(799, 4), 3039, 39]-NRT-code) | [i] | ||
| 4 | Linear OOA(3157, 799, F3, 5, 38) (dual of [(799, 5), 3838, 39]-NRT-code) | [i] | ||
| 5 | Digital (119, 157, 799)-net over F3 | [i] | ||