Information on Result #1324140
Linear OA(4229, 16448, F4, 41) (dual of [16448, 16219, 42]-code), using construction X with Varšamov bound based on
- linear OA(4225, 16441, F4, 41) (dual of [16441, 16216, 42]-code), using
- construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
- linear OA(4211, 16385, F4, 41) (dual of [16385, 16174, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4169, 16385, F4, 33) (dual of [16385, 16216, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
- linear OA(4225, 16444, F4, 39) (dual of [16444, 16219, 40]-code), using Gilbert–Varšamov bound and bm = 4225 > Vbs−1(k−1) = 39 913604 253862 018557 445467 237673 810467 725570 183871 850894 151821 244435 831805 021422 401010 315508 011632 659764 879643 007941 267129 677926 060954 [i]
- linear OA(41, 4, F4, 1) (dual of [4, 3, 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: 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(4229, 16448, F4, 2, 41) (dual of [(16448, 2), 32667, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4229, 16448, F4, 3, 41) (dual of [(16448, 3), 49115, 42]-NRT-code) | [i] | ||
| 3 | Digital (188, 229, 16448)-net over F4 | [i] | ||
| 4 | Linear OOA(4229, 8224, F4, 2, 41) (dual of [(8224, 2), 16219, 42]-NRT-code) | [i] | OOA Folding | |