Information on Result #1307564
Linear OA(450, 398, F4, 14) (dual of [398, 348, 15]-code), using 129 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 16 times 0, 1, 23 times 0, 1, 30 times 0, 1, 36 times 0) based on linear OA(441, 260, F4, 14) (dual of [260, 219, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(441, 256, F4, 14) (dual of [256, 215, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(437, 256, F4, 13) (dual of [256, 219, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 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(450, 398, F4, 2, 14) (dual of [(398, 2), 746, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(450, 398, F4, 3, 14) (dual of [(398, 3), 1144, 15]-NRT-code) | [i] | ||
| 3 | Digital (36, 50, 398)-net over F4 | [i] | ||