Information on Result #1419884
Linear OOA(424, 16395, F4, 2, 5) (dual of [(16395, 2), 32766, 6]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(424, 16395, F4, 5) (dual of [16395, 16371, 6]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(423, 16393, F4, 5) (dual of [16393, 16370, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- 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, 16384, F4, 3) (dual of [16384, 16369, 4]-code or 16384-cap in PG(14,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(423, 16394, F4, 4) (dual of [16394, 16371, 5]-code), using Gilbert–Varšamov bound and bm = 423 > Vbs−1(k−1) = 19 821423 675964 [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(423, 16393, F4, 5) (dual of [16393, 16370, 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(424, 16394, F4, 3, 5) (dual of [(16394, 3), 49158, 6]-NRT-code) | [i] | OOA Stacking with Additional Row | |
| 2 | Linear OOA(424, 16394, F4, 6, 5) (dual of [(16394, 6), 98340, 6]-NRT-code) | [i] | ||