Information on Result #704548
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]) 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: Constructive and 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 OA(3112, 749, F3, 27) (dual of [749, 637, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3111, 618, F3, 2, 27) (dual of [(618, 2), 1125, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3111, 618, F3, 3, 27) (dual of [(618, 3), 1743, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(3111, 618, F3, 4, 27) (dual of [(618, 4), 2361, 28]-NRT-code) | [i] | ||
| 5 | Linear OOA(3111, 618, F3, 5, 27) (dual of [(618, 5), 2979, 28]-NRT-code) | [i] | ||
| 6 | Digital (84, 111, 618)-net over F3 | [i] | ||
| 7 | Linear OA(3115, 761, F3, 27) (dual of [761, 646, 28]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(3116, 770, F3, 27) (dual of [770, 654, 28]-code) | [i] | ||
| 9 | Linear OA(3117, 784, F3, 27) (dual of [784, 667, 28]-code) | [i] | ||
| 10 | Linear OOA(3111, 374, F3, 2, 27) (dual of [(374, 2), 637, 28]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(3111, 249, F3, 3, 27) (dual of [(249, 3), 636, 28]-NRT-code) | [i] | ||
| 12 | Linear OOA(3111, 187, F3, 4, 27) (dual of [(187, 4), 637, 28]-NRT-code) | [i] | ||