Information on Result #1304436
Linear OA(3117, 784, F3, 27) (dual of [784, 667, 28]-code), using 30 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0) based on linear OA(3111, 748, F3, 27) (dual of [748, 637, 28]-code), using
- construction XX applied to C1 = C([725,22]), C2 = C([0,24]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C([725,24]) [i] based on
- 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 = {−3,−2,…,22}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(397, 728, F3, 25) (dual of [728, 631, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3109, 728, F3, 28) (dual of [728, 619, 29]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,24}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(391, 728, F3, 23) (dual of [728, 637, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 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(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 (see above)
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(3117, 784, F3, 2, 27) (dual of [(784, 2), 1451, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3117, 784, F3, 3, 27) (dual of [(784, 3), 2235, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(3117, 784, F3, 4, 27) (dual of [(784, 4), 3019, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(3117, 784, F3, 5, 27) (dual of [(784, 5), 3803, 28]-NRT-code) | [i] | ||
| 5 | Digital (90, 117, 784)-net over F3 | [i] | ||