Information on Result #704367
Linear OA(387, 748, F3, 21) (dual of [748, 661, 22]-code), using construction XX applied to C1 = C([725,16]), C2 = C([0,18]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([725,18]) based on
- linear OA(379, 728, F3, 20) (dual of [728, 649, 21]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,16}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(373, 728, F3, 19) (dual of [728, 655, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(385, 728, F3, 22) (dual of [728, 643, 23]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,18}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(367, 728, F3, 17) (dual of [728, 661, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [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(388, 749, F3, 21) (dual of [749, 661, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(387, 556, F3, 2, 21) (dual of [(556, 2), 1025, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(387, 556, F3, 3, 21) (dual of [(556, 3), 1581, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(387, 556, F3, 4, 21) (dual of [(556, 4), 2137, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(387, 556, F3, 5, 21) (dual of [(556, 5), 2693, 22]-NRT-code) | [i] | ||
| 6 | Digital (66, 87, 556)-net over F3 | [i] | ||
| 7 | Linear OOA(387, 374, F3, 2, 21) (dual of [(374, 2), 661, 22]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(387, 249, F3, 3, 21) (dual of [(249, 3), 660, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(387, 187, F3, 4, 21) (dual of [(187, 4), 661, 22]-NRT-code) | [i] | ||