Information on Result #2306479
Linear OA(3238, 6608, F3, 42) (dual of [6608, 6370, 43]-code), using 1 times code embedding in larger space based on linear OA(3237, 6607, F3, 42) (dual of [6607, 6370, 43]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3233, 6602, F3, 42) (dual of [6602, 6369, 43]-code), using
- construction X applied to C([0,21]) ⊂ C([0,18]) [i] based on
- linear OA(3225, 6562, F3, 43) (dual of [6562, 6337, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(38, 40, F3, 4) (dual of [40, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- construction X applied to C([0,21]) ⊂ C([0,18]) [i] based on
- linear OA(3233, 6603, F3, 38) (dual of [6603, 6370, 39]-code), using Gilbert–Varšamov bound and bm = 3233 > Vbs−1(k−1) = 19 261962 626123 021381 245112 919150 301814 699453 228446 961010 260547 580979 472108 117298 926487 333230 485815 607079 807401 [i]
- linear OA(33, 4, F3, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,3) or 4-cap in PG(2,3)), using
- dual of repetition code with length 4 [i]
- oval in PG(2, 3) [i]
- linear OA(3233, 6602, F3, 42) (dual of [6602, 6369, 43]-code), 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(3238, 3304, F3, 2, 42) (dual of [(3304, 2), 6370, 43]-NRT-code) | [i] | OOA Folding | |