Information on Result #1416004
Linear OOA(3213, 2075, F3, 2, 44) (dual of [(2075, 2), 3937, 45]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(3213, 2075, F3, 44) (dual of [2075, 1862, 45]-code), using
- discarding factors / shortening the dual code based on linear OA(3213, 2219, F3, 44) (dual of [2219, 2006, 45]-code), using
- construction XX applied to Ce(43) ⊂ Ce(39) ⊂ Ce(37) [i] based on
- linear OA(3204, 2187, F3, 44) (dual of [2187, 1983, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [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(3176, 2187, F3, 38) (dual of [2187, 2011, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(36, 29, F3, 3) (dual of [29, 23, 4]-code or 29-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [i]
- construction XX applied to Ce(43) ⊂ Ce(39) ⊂ Ce(37) [i] based on
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(3213, 1037, F3, 3, 44) (dual of [(1037, 3), 2898, 45]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3213, 1037, F3, 4, 44) (dual of [(1037, 4), 3935, 45]-NRT-code) | [i] | ||