Information on Result #1307485
Linear OA(439, 4126, F4, 8) (dual of [4126, 4087, 9]-code), using 15 step Varšamov–Edel lengthening with (ri) = (1, 14 times 0) based on linear OA(438, 4110, F4, 8) (dual of [4110, 4072, 9]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(437, 4096, F4, 9) (dual of [4096, 4059, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(425, 4096, F4, 6) (dual of [4096, 4071, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(439, 4126, F4, 2, 8) (dual of [(4126, 2), 8213, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(439, 4126, F4, 3, 8) (dual of [(4126, 3), 12339, 9]-NRT-code) | [i] | ||
| 3 | Digital (31, 39, 4126)-net over F4 | [i] | ||
| 4 | Linear OOA(439, 2063, F4, 2, 8) (dual of [(2063, 2), 4087, 9]-NRT-code) | [i] | OOA Folding | |