Information on Result #1307466
Linear OA(434, 4149, F4, 7) (dual of [4149, 4115, 8]-code), using 37 step Varšamov–Edel lengthening with (ri) = (1, 6 times 0, 1, 29 times 0) based on linear OA(432, 4110, F4, 7) (dual of [4110, 4078, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(431, 4096, F4, 7) (dual of [4096, 4065, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(419, 4096, F4, 5) (dual of [4096, 4077, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(413, 14, F4, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,4)), using
- dual of repetition code with length 14 [i]
- linear OA(41, 14, F4, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-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(434, 4149, F4, 2, 7) (dual of [(4149, 2), 8264, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(434, 4149, F4, 3, 7) (dual of [(4149, 3), 12413, 8]-NRT-code) | [i] | ||
| 3 | Digital (27, 34, 4149)-net over F4 | [i] | ||
| 4 | Linear OOA(434, 2074, F4, 2, 7) (dual of [(2074, 2), 4114, 8]-NRT-code) | [i] | OOA Folding | |