Information on Result #1420551
Linear OOA(470, 16413, F4, 2, 12) (dual of [(16413, 2), 32756, 13]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(470, 16413, F4, 12) (dual of [16413, 16343, 13]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(468, 16409, F4, 12) (dual of [16409, 16341, 13]-code), using
- 1 times truncation [i] based on linear OA(469, 16410, F4, 13) (dual of [16410, 16341, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(464, 16384, F4, 13) (dual of [16384, 16320, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(443, 16384, F4, 9) (dual of [16384, 16341, 10]-code), using an extension Ce(8) of 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(45, 26, F4, 3) (dual of [26, 21, 4]-code or 26-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- 1 times truncation [i] based on linear OA(469, 16410, F4, 13) (dual of [16410, 16341, 14]-code), using
- linear OA(468, 16411, F4, 11) (dual of [16411, 16343, 12]-code), using Gilbert–Varšamov bound and bm = 468 > Vbs−1(k−1) = 22984 360908 873290 560057 037615 529707 133496 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 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(468, 16409, F4, 12) (dual of [16409, 16341, 13]-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(470, 8206, F4, 3, 12) (dual of [(8206, 3), 24548, 13]-NRT-code) | [i] | OOA Folding | |