Information on Result #1466389
Linear OOA(3207, 4194381, F3, 2, 19) (dual of [(4194381, 2), 8388555, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(326, 80, F3, 2, 9) (dual of [(80, 2), 134, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(326, 80, F3, 9) (dual of [80, 54, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(326, 91, F3, 9) (dual of [91, 65, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(325, 82, F3, 9) (dual of [82, 57, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 82 | 38−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(317, 82, F3, 7) (dual of [82, 65, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 82 | 38−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(31, 9, F3, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(326, 91, F3, 9) (dual of [91, 65, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(326, 80, F3, 9) (dual of [80, 54, 10]-code), using
- linear OOA(3181, 4194301, F3, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- OOA 2-folding [i] based on linear OA(3181, 8388602, F3, 19) (dual of [8388602, 8388421, 20]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3207, 4194381, F3, 3, 19) (dual of [(4194381, 3), 12582936, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3207, 4194381, F3, 4, 19) (dual of [(4194381, 4), 16777317, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(3207, 4194381, F3, 5, 19) (dual of [(4194381, 5), 20971698, 20]-NRT-code) | [i] | ||
| 4 | Digital (188, 207, 4194381)-net over F3 | [i] | ||