Information on Result #676219
Linear OA(3118, 2209, F3, 24) (dual of [2209, 2091, 25]-code), using construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(19) based on
- 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(399, 2187, F3, 22) (dual of [2187, 2088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(392, 2187, F3, 20) (dual of [2187, 2095, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(3118, 1540, F3, 2, 24) (dual of [(1540, 2), 2962, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3118, 1540, F3, 3, 24) (dual of [(1540, 3), 4502, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(3118, 1540, F3, 4, 24) (dual of [(1540, 4), 6042, 25]-NRT-code) | [i] | ||
| 4 | Linear OOA(3118, 1540, F3, 5, 24) (dual of [(1540, 5), 7582, 25]-NRT-code) | [i] | ||
| 5 | Digital (94, 118, 1540)-net over F3 | [i] | ||
| 6 | Linear OOA(3118, 1104, F3, 2, 24) (dual of [(1104, 2), 2090, 25]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3118, 736, F3, 3, 24) (dual of [(736, 3), 2090, 25]-NRT-code) | [i] | ||
| 8 | Linear OOA(3118, 552, F3, 4, 24) (dual of [(552, 4), 2090, 25]-NRT-code) | [i] | ||