Information on Result #1316169
Linear OA(12831, 411, F128, 18) (dual of [411, 380, 19]-code), using 25 step Varšamov–Edel lengthening with (ri) = (1, 24 times 0) based on linear OA(12830, 385, F128, 18) (dual of [385, 355, 19]-code), using
- construction XX applied to C1 = C([380,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([380,16]) [i] based on
- linear OA(12828, 381, F128, 17) (dual of [381, 353, 18]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12828, 381, F128, 17) (dual of [381, 353, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12830, 381, F128, 18) (dual of [381, 351, 19]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(12826, 381, F128, 16) (dual of [381, 355, 17]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 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(12831, 411, F128, 2, 18) (dual of [(411, 2), 791, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12831, 411, F128, 3, 18) (dual of [(411, 3), 1202, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(12831, 411, F128, 4, 18) (dual of [(411, 4), 1613, 19]-NRT-code) | [i] | ||
| 4 | Digital (13, 31, 411)-net over F128 | [i] | ||