Information on Result #812724
Linear OOA(368, 88586, F3, 2, 9) (dual of [(88586, 2), 177104, 10]-NRT-code), using OOA 2-folding based on linear OA(368, 177172, F3, 9) (dual of [177172, 177104, 10]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(367, 177148, F3, 9) (dual of [177148, 177081, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(345, 177148, F3, 7) (dual of [177148, 177103, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(323, 24, F3, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,3)), using
- dual of repetition code with length 24 [i]
- linear OA(31, 24, F3, 1) (dual of [24, 23, 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
Mode: Constructive and 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(370, 88587, F3, 2, 9) (dual of [(88587, 2), 177104, 10]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(369, 88586, F3, 2, 9) (dual of [(88586, 2), 177103, 10]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(368, 88586, F3, 3, 9) (dual of [(88586, 3), 265690, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(368, 88586, F3, 4, 9) (dual of [(88586, 4), 354276, 10]-NRT-code) | [i] | ||
| 5 | Linear OOA(368, 88586, F3, 5, 9) (dual of [(88586, 5), 442862, 10]-NRT-code) | [i] | ||
| 6 | Digital (59, 68, 88586)-net over F3 | [i] | ||