Information on Result #1081222
Linear OOA(3235, large, F3, 4, 15), using (u, u+v)-construction based on
- linear OOA(37, 4, F3, 4, 7) (dual of [(4, 4), 9, 8]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;9,3) [i]
- linear OOA(3228, 8388600, F3, 4, 15) (dual of [(8388600, 4), 33554172, 16]-NRT-code), using
- trace code [i] based on linear OOA(8157, 2097150, F81, 4, 15) (dual of [(2097150, 4), 8388543, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8157, 8388600, F81, 15) (dual of [8388600, 8388543, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- OOA 4-folding [i] based on linear OA(8157, 8388600, F81, 15) (dual of [8388600, 8388543, 16]-code), using
- trace code [i] based on linear OOA(8157, 2097150, F81, 4, 15) (dual of [(2097150, 4), 8388543, 16]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m 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(3235, large, F3, 4, 14) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3235, large, F3, 4, 13) | [i] | ||
| 3 | Linear OOA(3235, large, F3, 4, 12) | [i] | ||
| 4 | Linear OOA(3235, large, F3, 4, 11) | [i] | ||
| 5 | Linear OOA(3235, large, F3, 4, 10) | [i] | ||
| 6 | Linear OOA(3235, large, F3, 4, 9) | [i] | ||
| 7 | Linear OOA(3235, large, F3, 4, 8) | [i] | ||
| 8 | Linear OOA(3235, large, F3, 4, 7) | [i] | ||
| 9 | Linear OOA(3235, large, F3, 4, 6) | [i] | ||
| 10 | Linear OOA(3235, large, F3, 4, 5) | [i] | ||
| 11 | Linear OOA(3235, large, F3, 4, 4) | [i] | ||
| 12 | Linear OOA(3235, large, F3, 4, 3) | [i] | ||
| 13 | Linear OOA(3239, large, F3, 4, 15) | [i] | NRT-Code Embedding in Larger Space | |
| 14 | Linear OOA(3243, large, F3, 4, 15) | [i] | ||
| 15 | Linear OOA(3247, large, F3, 4, 15) | [i] | ||
| 16 | Linear OOA(3237, large, F3, 4, 15) | [i] | OOA Duplication | |
| 17 | Linear OOA(3238, large, F3, 4, 15) | [i] | ||
| 18 | Linear OOA(3235, 4194301, F3, 20, 15) (dual of [(4194301, 20), 83885785, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |