Information on Result #677920
Linear OA(435, 4194316, F4, 5) (dual of [4194316, 4194281, 6]-code), using construction X applied to Ce(4) ⊂ Ce(2) based on
- linear OA(434, 4194304, F4, 5) (dual of [4194304, 4194270, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(423, 4194304, F4, 3) (dual of [4194304, 4194281, 4]-code or 4194304-cap in PG(22,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(41, 12, F4, 1) (dual of [12, 11, 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(435, 4032821, F4, 2, 5) (dual of [(4032821, 2), 8065607, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(435, 4032821, F4, 3, 5) (dual of [(4032821, 3), 12098428, 6]-NRT-code) | [i] | ||
| 3 | Digital (30, 35, 4032821)-net over F4 | [i] | ||
| 4 | Linear OOA(435, 2097158, F4, 2, 5) (dual of [(2097158, 2), 4194281, 6]-NRT-code) | [i] | OOA Folding | |