Information on Result #1299657
Linear OA(3245, 19748, F3, 38) (dual of [19748, 19503, 39]-code), using construction X with Varšamov bound based on
- linear OA(3241, 19743, F3, 38) (dual of [19743, 19502, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(30) [i] based on
- linear OA(3226, 19683, F3, 38) (dual of [19683, 19457, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3181, 19683, F3, 31) (dual of [19683, 19502, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(315, 60, F3, 6) (dual of [60, 45, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- construction X applied to Ce(37) ⊂ Ce(30) [i] based on
- linear OA(3241, 19744, F3, 34) (dual of [19744, 19503, 35]-code), using Gilbert–Varšamov bound and bm = 3241 > Vbs−1(k−1) = 5 403568 492093 156251 309908 229410 977095 592381 407719 839200 528675 647364 724887 398166 906241 616176 827087 399054 826839 684651 [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]
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 OA(3246, 19749, F3, 38) (dual of [19749, 19503, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3245, 9874, F3, 2, 38) (dual of [(9874, 2), 19503, 39]-NRT-code) | [i] | OOA Folding | |