Information on Result #679105
Linear OA(437, 16400, F4, 7) (dual of [16400, 16363, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(4) based on
- linear OA(436, 16384, F4, 7) (dual of [16384, 16348, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(422, 16384, F4, 5) (dual of [16384, 16362, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(415, 16, F4, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,4)), using
- dual of repetition code with length 16 [i]
- linear OA(41, 16, F4, 1) (dual of [16, 15, 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: 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 OA(438, 16401, F4, 7) (dual of [16401, 16363, 8]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(439, 16402, F4, 7) (dual of [16402, 16363, 8]-code) | [i] | ||
| 3 | Linear OOA(437, 16400, F4, 2, 7) (dual of [(16400, 2), 32763, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(437, 16400, F4, 3, 7) (dual of [(16400, 3), 49163, 8]-NRT-code) | [i] | ||
| 5 | Digital (30, 37, 16400)-net over F4 | [i] | ||
| 6 | Linear OA(438, 16402, F4, 7) (dual of [16402, 16364, 8]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(439, 16404, F4, 7) (dual of [16404, 16365, 8]-code) | [i] | ||
| 8 | Linear OOA(437, 8200, F4, 2, 7) (dual of [(8200, 2), 16363, 8]-NRT-code) | [i] | OOA Folding | |