Information on Result #1305239
Linear OA(3213, 2299, F3, 43) (dual of [2299, 2086, 44]-code), using 89 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 7 times 0, 1, 9 times 0, 1, 12 times 0, 1, 17 times 0, 1, 21 times 0) based on linear OA(3198, 2195, F3, 43) (dual of [2195, 1997, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(40) [i] based on
- 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(3190, 2187, F3, 41) (dual of [2187, 1997, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(31, 8, F3, 1) (dual of [8, 7, 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
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(3213, 2299, F3, 2, 43) (dual of [(2299, 2), 4385, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3213, 2299, F3, 3, 43) (dual of [(2299, 3), 6684, 44]-NRT-code) | [i] | ||
| 3 | Linear OOA(3213, 2299, F3, 4, 43) (dual of [(2299, 4), 8983, 44]-NRT-code) | [i] | ||
| 4 | Linear OOA(3213, 2299, F3, 5, 43) (dual of [(2299, 5), 11282, 44]-NRT-code) | [i] | ||
| 5 | Digital (170, 213, 2299)-net over F3 | [i] | ||
| 6 | Linear OOA(3213, 1149, F3, 2, 43) (dual of [(1149, 2), 2085, 44]-NRT-code) | [i] | OOA Folding | |