Information on Result #1419960
Linear OOA(433, 1048590, F4, 2, 5) (dual of [(1048590, 2), 2097147, 6]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(433, 1048590, F4, 5) (dual of [1048590, 1048557, 6]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(432, 1048588, F4, 5) (dual of [1048588, 1048556, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(431, 1048576, F4, 5) (dual of [1048576, 1048545, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(421, 1048576, F4, 3) (dual of [1048576, 1048555, 4]-code or 1048576-cap in PG(20,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(411, 12, F4, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,4)), using
- dual of repetition code with length 12 [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
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(432, 1048589, F4, 4) (dual of [1048589, 1048557, 5]-code), using Gilbert–Varšamov bound and bm = 432 > Vbs−1(k−1) = 5 188314 997829 671339 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(432, 1048588, F4, 5) (dual of [1048588, 1048556, 6]-code), 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(433, 1048589, F4, 3, 5) (dual of [(1048589, 3), 3145734, 6]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(433, 1048589, F4, 6, 5) (dual of [(1048589, 6), 6291501, 6]-NRT-code) | [i] | ||