Information on Result #1323952
Linear OA(4157, 16445, F4, 27) (dual of [16445, 16288, 28]-code), using construction X with Varšamov bound based on
- linear OA(4155, 16441, F4, 27) (dual of [16441, 16286, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,9]) [i] based on
- linear OA(4141, 16385, F4, 27) (dual of [16385, 16244, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(499, 16385, F4, 19) (dual of [16385, 16286, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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([0,13]) ⊂ C([0,9]) [i] based on
- linear OA(4155, 16443, F4, 26) (dual of [16443, 16288, 27]-code), using Gilbert–Varšamov bound and bm = 4155 > Vbs−1(k−1) = 134 444864 235052 168053 708160 129687 976636 264203 356704 717389 555951 611310 085523 167911 162508 013805 [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
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(4157, 16445, F4, 2, 27) (dual of [(16445, 2), 32733, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4157, 16445, F4, 3, 27) (dual of [(16445, 3), 49178, 28]-NRT-code) | [i] | ||
| 3 | Digital (130, 157, 16445)-net over F4 | [i] | ||
| 4 | Linear OOA(4157, 8222, F4, 2, 27) (dual of [(8222, 2), 16287, 28]-NRT-code) | [i] | OOA Folding | |