Information on Result #704469
Linear OA(3118, 763, F3, 28) (dual of [763, 645, 29]-code), using construction XX applied to C1 = C([722,19]), C2 = C([0,21]), C3 = C1 + C2 = C([0,19]), and C∩ = C1 ∩ C2 = C([722,21]) 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 = {−6,−5,…,19}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(385, 728, F3, 22) (dual of [728, 643, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [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 = {−6,−5,…,21}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(379, 728, F3, 20) (dual of [728, 649, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- 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: 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(3119, 764, F3, 28) (dual of [764, 645, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3118, 717, F3, 2, 28) (dual of [(717, 2), 1316, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3118, 717, F3, 3, 28) (dual of [(717, 3), 2033, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(3118, 717, F3, 4, 28) (dual of [(717, 4), 2750, 29]-NRT-code) | [i] | ||
| 5 | Linear OOA(3118, 717, F3, 5, 28) (dual of [(717, 5), 3467, 29]-NRT-code) | [i] | ||
| 6 | Digital (90, 118, 717)-net over F3 | [i] | ||
| 7 | Linear OA(3119, 765, F3, 28) (dual of [765, 646, 29]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OOA(3118, 381, F3, 2, 28) (dual of [(381, 2), 644, 29]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(3118, 254, F3, 3, 28) (dual of [(254, 3), 644, 29]-NRT-code) | [i] | ||