Information on Result #1304389
Linear OA(3116, 857, F3, 26) (dual of [857, 741, 27]-code), using 104 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 1, 0, 0, 0, 1, 6 times 0, 1, 8 times 0, 1, 12 times 0, 1, 16 times 0, 1, 21 times 0, 1, 26 times 0) based on linear OA(3104, 741, F3, 26) (dual of [741, 637, 27]-code), using
- construction XX applied to C1 = C([340,364]), C2 = C([342,365]), C3 = C1 + C2 = C([342,364]), and C∩ = C1 ∩ C2 = C([340,365]) [i] based on
- linear OA(397, 728, F3, 25) (dual of [728, 631, 26]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {340,341,…,364}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(397, 728, F3, 24) (dual of [728, 631, 25]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {342,343,…,365}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3103, 728, F3, 26) (dual of [728, 625, 27]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {340,341,…,365}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(391, 728, F3, 23) (dual of [728, 637, 24]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {342,343,…,364}, and designed minimum distance d ≥ |I|+1 = 24 [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(3116, 857, F3, 2, 26) (dual of [(857, 2), 1598, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3116, 857, F3, 3, 26) (dual of [(857, 3), 2455, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(3116, 857, F3, 4, 26) (dual of [(857, 4), 3312, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(3116, 857, F3, 5, 26) (dual of [(857, 5), 4169, 27]-NRT-code) | [i] | ||
| 5 | Digital (90, 116, 857)-net over F3 | [i] | ||