Information on Result #1304594
Linear OA(3132, 803, F3, 31) (dual of [803, 671, 32]-code), using 54 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 8 times 0, 1, 10 times 0, 1, 13 times 0) based on linear OA(3119, 736, F3, 31) (dual of [736, 617, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(3118, 729, F3, 31) (dual of [729, 611, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3112, 729, F3, 29) (dual of [729, 617, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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
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(3132, 803, F3, 2, 31) (dual of [(803, 2), 1474, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3132, 803, F3, 3, 31) (dual of [(803, 3), 2277, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3132, 803, F3, 4, 31) (dual of [(803, 4), 3080, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(3132, 803, F3, 5, 31) (dual of [(803, 5), 3883, 32]-NRT-code) | [i] | ||
| 5 | Digital (101, 132, 803)-net over F3 | [i] | ||