Information on Result #1299314
Linear OA(3209, 19748, F3, 32) (dual of [19748, 19539, 33]-code), using construction X with Varšamov bound based on
- linear OA(3205, 19743, F3, 32) (dual of [19743, 19538, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(24) [i] based on
- linear OA(3190, 19683, F3, 32) (dual of [19683, 19493, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(31) ⊂ Ce(24) [i] based on
- linear OA(3205, 19744, F3, 28) (dual of [19744, 19539, 29]-code), using Gilbert–Varšamov bound and bm = 3205 > Vbs−1(k−1) = 1 146977 584972 724527 167431 877503 374008 689045 769572 203204 637508 927853 650463 865575 605521 413411 911211 [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(3210, 19749, F3, 32) (dual of [19749, 19539, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3209, 9874, F3, 2, 32) (dual of [(9874, 2), 19539, 33]-NRT-code) | [i] | OOA Folding | |