Information on Result #704237
Linear OA(363, 748, F3, 15) (dual of [748, 685, 16]-code), using construction XX applied to C1 = C([725,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([725,12]) based on
- linear OA(355, 728, F3, 14) (dual of [728, 673, 15]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,10}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(349, 728, F3, 13) (dual of [728, 679, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(361, 728, F3, 16) (dual of [728, 667, 17]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−3,−2,…,12}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(343, 728, F3, 11) (dual of [728, 685, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [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(364, 749, F3, 15) (dual of [749, 685, 16]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(363, 523, F3, 2, 15) (dual of [(523, 2), 983, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(363, 523, F3, 3, 15) (dual of [(523, 3), 1506, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(363, 523, F3, 4, 15) (dual of [(523, 4), 2029, 16]-NRT-code) | [i] | ||
| 5 | Linear OOA(363, 523, F3, 5, 15) (dual of [(523, 5), 2552, 16]-NRT-code) | [i] | ||
| 6 | Digital (48, 63, 523)-net over F3 | [i] | ||
| 7 | Linear OA(367, 761, F3, 15) (dual of [761, 694, 16]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OOA(363, 374, F3, 2, 15) (dual of [(374, 2), 685, 16]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(363, 249, F3, 3, 15) (dual of [(249, 3), 684, 16]-NRT-code) | [i] | ||
| 10 | Linear OOA(363, 187, F3, 4, 15) (dual of [(187, 4), 685, 16]-NRT-code) | [i] | ||