Information on Result #675399
Linear OA(3107, 6598, F3, 19) (dual of [6598, 6491, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,6]) based on
- linear OA(397, 6562, F3, 19) (dual of [6562, 6465, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(365, 6562, F3, 13) (dual of [6562, 6497, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(310, 36, F3, 5) (dual of [36, 26, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(31, 12, F3, 1) (dual of [12, 11, 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
- linear OA(33, 12, F3, 2) (dual of [12, 9, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- discarding factors / shortening the dual code based on linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- linear OA(36, 12, F3, 5) (dual of [12, 6, 6]-code), using
- extended Golay code Ge(3) [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- (u, u−v, u+v+w)-construction [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(3107, 3372, F3, 2, 19) (dual of [(3372, 2), 6637, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3107, 3372, F3, 3, 19) (dual of [(3372, 3), 10009, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(3107, 3372, F3, 4, 19) (dual of [(3372, 4), 13381, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(3107, 3372, F3, 5, 19) (dual of [(3372, 5), 16753, 20]-NRT-code) | [i] | ||
| 5 | Digital (88, 107, 3372)-net over F3 | [i] | ||
| 6 | Linear OOA(3107, 733, F3, 19, 19) (dual of [(733, 19), 13820, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |