Information on Result #2306453
Linear OA(3228, 19749, F3, 35) (dual of [19749, 19521, 36]-code), using 1 times code embedding in larger space based on linear OA(3227, 19748, F3, 35) (dual of [19748, 19521, 36]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3223, 19743, F3, 35) (dual of [19743, 19520, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(27) [i] based on
- linear OA(3208, 19683, F3, 35) (dual of [19683, 19475, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(34) ⊂ Ce(27) [i] based on
- linear OA(3223, 19744, F3, 31) (dual of [19744, 19521, 32]-code), using Gilbert–Varšamov bound and bm = 3223 > Vbs−1(k−1) = 2886 629793 865856 283191 067612 105477 032392 604255 992285 397002 261094 876046 791421 129220 798565 283279 576058 508843 [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(3223, 19743, F3, 35) (dual of [19743, 19520, 36]-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(3228, 6583, F3, 3, 35) (dual of [(6583, 3), 19521, 36]-NRT-code) | [i] | OOA Folding | |