Information on Result #1304101
Linear OA(340, 751, F3, 9) (dual of [751, 711, 10]-code), using 8 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0) based on linear OA(337, 740, F3, 9) (dual of [740, 703, 10]-code), using
- construction XX applied to C1 = C([727,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([727,7]) [i] based on
- linear OA(331, 728, F3, 8) (dual of [728, 697, 9]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(331, 728, F3, 8) (dual of [728, 697, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(337, 728, F3, 9) (dual of [728, 691, 10]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(325, 728, F3, 7) (dual of [728, 703, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code) (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(340, 751, F3, 2, 9) (dual of [(751, 2), 1462, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(340, 751, F3, 3, 9) (dual of [(751, 3), 2213, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(340, 751, F3, 4, 9) (dual of [(751, 4), 2964, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(340, 751, F3, 5, 9) (dual of [(751, 5), 3715, 10]-NRT-code) | [i] | ||
| 5 | Digital (31, 40, 751)-net over F3 | [i] | ||