Information on Result #1305179
Linear OA(3209, 2288, F3, 42) (dual of [2288, 2079, 43]-code), using 75 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 7 times 0, 1, 11 times 0, 1, 16 times 0, 1, 23 times 0) based on linear OA(3198, 2202, F3, 42) (dual of [2202, 2004, 43]-code), using
- construction X applied to Ce(42) ⊂ Ce(39) [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(3183, 2187, F3, 40) (dual of [2187, 2004, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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(3209, 2288, F3, 2, 42) (dual of [(2288, 2), 4367, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3209, 2288, F3, 3, 42) (dual of [(2288, 3), 6655, 43]-NRT-code) | [i] | ||
| 3 | Linear OOA(3209, 2288, F3, 4, 42) (dual of [(2288, 4), 8943, 43]-NRT-code) | [i] | ||
| 4 | Linear OOA(3209, 2288, F3, 5, 42) (dual of [(2288, 5), 11231, 43]-NRT-code) | [i] | ||
| 5 | Digital (167, 209, 2288)-net over F3 | [i] | ||
| 6 | Linear OOA(3209, 1144, F3, 2, 42) (dual of [(1144, 2), 2079, 43]-NRT-code) | [i] | OOA Folding | |