Information on Result #1323950
Linear OA(4156, 16443, F4, 27) (dual of [16443, 16287, 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, 16442, F4, 26) (dual of [16442, 16287, 27]-code), using Gilbert–Varšamov bound and bm = 4155 > Vbs−1(k−1) = 134 240445 470095 403677 994777 843457 811180 218729 071063 270399 071730 372963 130593 570484 047791 420912 [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
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(4156, 16443, F4, 2, 27) (dual of [(16443, 2), 32730, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4156, 16443, F4, 3, 27) (dual of [(16443, 3), 49173, 28]-NRT-code) | [i] | ||
| 3 | Digital (129, 156, 16443)-net over F4 | [i] | ||
| 4 | Linear OOA(4156, 8221, F4, 2, 27) (dual of [(8221, 2), 16286, 28]-NRT-code) | [i] | OOA Folding | |