Information on Result #1527127
Linear OOA(3189, 8652, F3, 3, 31) (dual of [(8652, 3), 25767, 32]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3189, 8652, F3, 2, 31) (dual of [(8652, 2), 17115, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3189, 9859, F3, 2, 31) (dual of [(9859, 2), 19529, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3189, 19718, F3, 31) (dual of [19718, 19529, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- 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(3154, 19683, F3, 26) (dual of [19683, 19529, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(38, 35, F3, 4) (dual of [35, 27, 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 Ce(30) ⊂ Ce(25) [i] based on
- OOA 2-folding [i] based on linear OA(3189, 19718, F3, 31) (dual of [19718, 19529, 32]-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(3189, 4326, F3, 5, 31) (dual of [(4326, 5), 21441, 32]-NRT-code) | [i] | OOA Folding | |