Information on Result #1524509
Linear OOA(3153, 8502, F3, 3, 25) (dual of [(8502, 3), 25353, 26]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3153, 8502, F3, 2, 25) (dual of [(8502, 2), 16851, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3153, 9859, F3, 2, 25) (dual of [(9859, 2), 19565, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3153, 19718, F3, 25) (dual of [19718, 19565, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- 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(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(24) ⊂ Ce(19) [i] based on
- OOA 2-folding [i] based on linear OA(3153, 19718, F3, 25) (dual of [19718, 19565, 26]-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(3153, 4251, F3, 5, 25) (dual of [(4251, 5), 21102, 26]-NRT-code) | [i] | OOA Folding | |