Information on Result #1304165
Linear OA(363, 278, F3, 17) (dual of [278, 215, 18]-code), using 19 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 7 times 0) based on linear OA(357, 253, F3, 17) (dual of [253, 196, 18]-code), using
- construction XX applied to C1 = C([106,121]), C2 = C([108,122]), C3 = C1 + C2 = C([108,121]), and C∩ = C1 ∩ C2 = C([106,122]) [i] based on
- linear OA(351, 242, F3, 16) (dual of [242, 191, 17]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {106,107,…,121}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(351, 242, F3, 15) (dual of [242, 191, 16]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {108,109,…,122}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(356, 242, F3, 17) (dual of [242, 186, 18]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {106,107,…,122}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(346, 242, F3, 14) (dual of [242, 196, 15]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {108,109,…,121}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 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(30, 5, F3, 0) (dual of [5, 5, 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
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(363, 278, F3, 2, 17) (dual of [(278, 2), 493, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(363, 278, F3, 3, 17) (dual of [(278, 3), 771, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(363, 278, F3, 4, 17) (dual of [(278, 4), 1049, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(363, 278, F3, 5, 17) (dual of [(278, 5), 1327, 18]-NRT-code) | [i] | ||
| 5 | Digital (46, 63, 278)-net over F3 | [i] | ||