Information on Result #2486045
Linear OOA(3113, 88586, F3, 2, 15) (dual of [(88586, 2), 177059, 16]-NRT-code), using 31 times duplication based on linear OOA(3112, 88586, F3, 2, 15) (dual of [(88586, 2), 177060, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3112, 177172, F3, 15) (dual of [177172, 177060, 16]-code), using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(3111, 177148, F3, 15) (dual of [177148, 177037, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(389, 177148, F3, 13) (dual of [177148, 177059, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
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(3113, 68491, F3, 3, 15) (dual of [(68491, 3), 205360, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3113, 68491, F3, 4, 15) (dual of [(68491, 4), 273851, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(3113, 68491, F3, 5, 15) (dual of [(68491, 5), 342342, 16]-NRT-code) | [i] | ||
| 4 | Digital (98, 113, 68491)-net over F3 | [i] | ||