Information on Result #679384
Linear OA(443, 16392, F4, 8) (dual of [16392, 16349, 9]-code), using construction X4 applied to C([1,8]) ⊂ C([1,6]) based on
- linear OA(442, 16383, F4, 8) (dual of [16383, 16341, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(435, 16383, F4, 6) (dual of [16383, 16348, 7]-code), using 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(48, 9, F4, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,4)), using
- dual of repetition code with length 9 [i]
- linear OA(41, 9, F4, 1) (dual of [9, 8, 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 OOA(443, 16346, F4, 2, 8) (dual of [(16346, 2), 32649, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(443, 16346, F4, 3, 8) (dual of [(16346, 3), 48995, 9]-NRT-code) | [i] | ||
| 3 | Digital (35, 43, 16346)-net over F4 | [i] | ||
| 4 | Linear OOA(443, 8196, F4, 2, 8) (dual of [(8196, 2), 16349, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(443, 5464, F4, 3, 8) (dual of [(5464, 3), 16349, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(443, 4098, F4, 8, 8) (dual of [(4098, 8), 32741, 9]-NRT-code) | [i] | OA Folding and Stacking | |