Information on Result #1304633
Linear OA(3137, 824, F3, 32) (dual of [824, 687, 33]-code), using 71 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 8 times 0, 1, 10 times 0, 1, 14 times 0, 1, 18 times 0) based on linear OA(3125, 741, F3, 32) (dual of [741, 616, 33]-code), using
- construction XX applied to C1 = C([334,364]), C2 = C([336,365]), C3 = C1 + C2 = C([336,364]), and C∩ = C1 ∩ C2 = C([334,365]) [i] based on
- linear OA(3118, 728, F3, 31) (dual of [728, 610, 32]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {334,335,…,364}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3118, 728, F3, 30) (dual of [728, 610, 31]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,365}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3124, 728, F3, 32) (dual of [728, 604, 33]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {334,335,…,365}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3112, 728, F3, 29) (dual of [728, 616, 30]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {336,337,…,364}, and designed minimum distance d ≥ |I|+1 = 30 [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(3137, 824, F3, 2, 32) (dual of [(824, 2), 1511, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3137, 824, F3, 3, 32) (dual of [(824, 3), 2335, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(3137, 824, F3, 4, 32) (dual of [(824, 4), 3159, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(3137, 824, F3, 5, 32) (dual of [(824, 5), 3983, 33]-NRT-code) | [i] | ||
| 5 | Digital (105, 137, 824)-net over F3 | [i] | ||