Information on Result #1304228
Linear OA(373, 285, F3, 20) (dual of [285, 212, 21]-code), using 26 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 9 times 0) based on linear OA(367, 253, F3, 20) (dual of [253, 186, 21]-code), using
- construction XX applied to C1 = C([103,121]), C2 = C([105,122]), C3 = C1 + C2 = C([105,121]), and C∩ = C1 ∩ C2 = C([103,122]) [i] based on
- linear OA(361, 242, F3, 19) (dual of [242, 181, 20]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {103,104,…,121}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(361, 242, F3, 18) (dual of [242, 181, 19]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {105,106,…,122}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(366, 242, F3, 20) (dual of [242, 176, 21]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {103,104,…,122}, and designed minimum distance d ≥ |I|+1 = 21 [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 = {105,106,…,121}, and designed minimum distance d ≥ |I|+1 = 18 [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(373, 285, F3, 2, 20) (dual of [(285, 2), 497, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(373, 285, F3, 3, 20) (dual of [(285, 3), 782, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(373, 285, F3, 4, 20) (dual of [(285, 4), 1067, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(373, 285, F3, 5, 20) (dual of [(285, 5), 1352, 21]-NRT-code) | [i] | ||
| 5 | Digital (53, 73, 285)-net over F3 | [i] | ||