Information on Result #812733
Linear OOA(386, 2391500, F3, 2, 9) (dual of [(2391500, 2), 4782914, 10]-NRT-code), using OOA 2-folding based on linear OA(386, 4783000, F3, 9) (dual of [4783000, 4782914, 10]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(385, 4782970, F3, 9) (dual of [4782970, 4782885, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(357, 4782970, F3, 7) (dual of [4782970, 4782913, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(329, 30, F3, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
- dual of repetition code with length 30 [i]
- linear OA(31, 30, F3, 1) (dual of [30, 29, 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(388, 2391501, F3, 2, 9) (dual of [(2391501, 2), 4782914, 10]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(387, 2391500, F3, 2, 9) (dual of [(2391500, 2), 4782913, 10]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3114, 4782985, F3, 2, 9) (dual of [(4782985, 2), 9565856, 10]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 4 | Linear OOA(3115, 4783000, F3, 2, 9) (dual of [(4783000, 2), 9565885, 10]-NRT-code) | [i] | ||
| 5 | Linear OOA(386, 2391500, F3, 3, 9) (dual of [(2391500, 3), 7174414, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(386, 2391500, F3, 4, 9) (dual of [(2391500, 4), 9565914, 10]-NRT-code) | [i] | ||
| 7 | Linear OOA(386, 2391500, F3, 5, 9) (dual of [(2391500, 5), 11957414, 10]-NRT-code) | [i] | ||
| 8 | Digital (77, 86, 2391500)-net over F3 | [i] | ||