Information on Result #700193
Linear OA(12827, 386, F128, 16) (dual of [386, 359, 17]-code), using construction X applied to Ce(15) ⊂ Ce(13) based on
- linear OA(12826, 382, F128, 16) (dual of [382, 356, 17]-code), using an extension Ce(15) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12823, 382, F128, 14) (dual of [382, 359, 15]-code), using an extension Ce(13) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(1281, 4, F128, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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 OOA(12827, 384, F128, 2, 16) (dual of [(384, 2), 741, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12827, 384, F128, 3, 16) (dual of [(384, 3), 1125, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(12827, 384, F128, 4, 16) (dual of [(384, 4), 1509, 17]-NRT-code) | [i] | ||
| 4 | Digital (11, 27, 384)-net over F128 | [i] | ||
| 5 | Linear OA(12828, 445, F128, 16) (dual of [445, 417, 17]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OOA(12827, 193, F128, 2, 16) (dual of [(193, 2), 359, 17]-NRT-code) | [i] | OOA Folding | |