Information on Result #678684
Linear OA(436, 65555, F4, 6) (dual of [65555, 65519, 7]-code), using construction X applied to Ce(5) ⊂ Ce(2) based on
- linear OA(433, 65536, F4, 6) (dual of [65536, 65503, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(417, 65536, F4, 3) (dual of [65536, 65519, 4]-code or 65536-cap in PG(16,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(43, 19, F4, 2) (dual of [19, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), 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(436, 65555, F4, 2, 6) (dual of [(65555, 2), 131074, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(436, 65555, F4, 3, 6) (dual of [(65555, 3), 196629, 7]-NRT-code) | [i] | ||
| 3 | Digital (30, 36, 65555)-net over F4 | [i] | ||
| 4 | Linear OOA(436, 32777, F4, 2, 6) (dual of [(32777, 2), 65518, 7]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(436, 21851, F4, 3, 6) (dual of [(21851, 3), 65517, 7]-NRT-code) | [i] | ||