Information on Result #704788
Linear OA(3151, 763, F3, 37) (dual of [763, 612, 38]-code), using construction XX applied to C1 = C([722,28]), C2 = C([0,30]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([722,30]) based on
- linear OA(3136, 728, F3, 35) (dual of [728, 592, 36]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,28}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(3118, 728, F3, 31) (dual of [728, 610, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3142, 728, F3, 37) (dual of [728, 586, 38]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,30}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3112, 728, F3, 29) (dual of [728, 616, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [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 OOA(3151, 740, F3, 2, 37) (dual of [(740, 2), 1329, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3151, 740, F3, 3, 37) (dual of [(740, 3), 2069, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(3151, 740, F3, 4, 37) (dual of [(740, 4), 2809, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(3151, 740, F3, 5, 37) (dual of [(740, 5), 3549, 38]-NRT-code) | [i] | ||
| 5 | Digital (114, 151, 740)-net over F3 | [i] | ||
| 6 | Linear OOA(3151, 381, F3, 2, 37) (dual of [(381, 2), 611, 38]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3151, 254, F3, 3, 37) (dual of [(254, 3), 611, 38]-NRT-code) | [i] | ||