Information on Result #1305288
Linear OA(3216, 2258, F3, 44) (dual of [2258, 2042, 45]-code), using 52 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 7 times 0, 1, 11 times 0, 1, 15 times 0) based on linear OA(3204, 2194, F3, 44) (dual of [2194, 1990, 45]-code), using
- construction X applied to Ce(43) ⊂ Ce(42) [i] based on
- linear OA(3204, 2187, F3, 44) (dual of [2187, 1983, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3197, 2187, F3, 43) (dual of [2187, 1990, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(30, 7, F3, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(3216, 2247, F3, 2, 44) (dual of [(2247, 2), 4278, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3216, 2247, F3, 3, 44) (dual of [(2247, 3), 6525, 45]-NRT-code) | [i] | ||
| 3 | Linear OOA(3216, 2247, F3, 4, 44) (dual of [(2247, 4), 8772, 45]-NRT-code) | [i] | ||
| 4 | Linear OOA(3216, 2247, F3, 5, 44) (dual of [(2247, 5), 11019, 45]-NRT-code) | [i] | ||
| 5 | Digital (172, 216, 2247)-net over F3 | [i] | ||
| 6 | Linear OOA(3216, 1129, F3, 2, 44) (dual of [(1129, 2), 2042, 45]-NRT-code) | [i] | OOA Folding | |