Information on Result #676210
Linear OA(3132, 2209, F3, 27) (dual of [2209, 2077, 28]-code), using construction XX applied to Ce(27) ⊂ Ce(24) ⊂ Ce(22) based on
- linear OA(3127, 2187, F3, 28) (dual of [2187, 2060, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3113, 2187, F3, 25) (dual of [2187, 2074, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3106, 2187, F3, 23) (dual of [2187, 2081, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(31, 18, F3, 1) (dual of [18, 17, 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(31, 4, F3, 1) (dual of [4, 3, 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 (see above)
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(3132, 1586, F3, 2, 27) (dual of [(1586, 2), 3040, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3132, 1586, F3, 3, 27) (dual of [(1586, 3), 4626, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(3132, 1586, F3, 4, 27) (dual of [(1586, 4), 6212, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(3132, 1586, F3, 5, 27) (dual of [(1586, 5), 7798, 28]-NRT-code) | [i] | ||
| 5 | Digital (105, 132, 1586)-net over F3 | [i] | ||
| 6 | Linear OOA(3132, 1104, F3, 2, 27) (dual of [(1104, 2), 2076, 28]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3132, 736, F3, 3, 27) (dual of [(736, 3), 2076, 28]-NRT-code) | [i] | ||
| 8 | Linear OOA(3132, 552, F3, 4, 27) (dual of [(552, 4), 2076, 28]-NRT-code) | [i] | ||