Information on Result #674641
Linear OA(3139, 177176, F3, 19) (dual of [177176, 177037, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,7]) based on
- linear OA(3133, 177148, F3, 19) (dual of [177148, 177015, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 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(36, 28, F3, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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 OA(3140, 177177, F3, 19) (dual of [177177, 177037, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3138, 177175, F3, 18) (dual of [177175, 177037, 19]-code) | [i] | Truncation | |
| 3 | Linear OOA(3139, 88588, F3, 2, 19) (dual of [(88588, 2), 177037, 20]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3139, 44294, F3, 4, 19) (dual of [(44294, 4), 177037, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(3139, 35435, F3, 5, 19) (dual of [(35435, 5), 177036, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(3139, 19686, F3, 19, 19) (dual of [(19686, 19), 373895, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |