Information on Result #895248
Linear OOA(3223, 4195398, F3, 2, 18) (dual of [(4195398, 2), 8390573, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(343, 1097, F3, 2, 9) (dual of [(1097, 2), 2151, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(343, 2194, F3, 9) (dual of [2194, 2151, 10]-code), using
- 1 times truncation [i] based on linear OA(344, 2195, F3, 10) (dual of [2195, 2151, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(343, 2187, F3, 10) (dual of [2187, 2144, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(336, 2187, F3, 8) (dual of [2187, 2151, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(31, 8, F3, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- 1 times truncation [i] based on linear OA(344, 2195, F3, 10) (dual of [2195, 2151, 11]-code), using
- OOA 2-folding [i] based on linear OA(343, 2194, F3, 9) (dual of [2194, 2151, 10]-code), using
- linear OOA(3180, 4194301, F3, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3180, 8388602, F3, 18) (dual of [8388602, 8388422, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- OOA 2-folding [i] based on linear OA(3180, 8388602, F3, 18) (dual of [8388602, 8388422, 19]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3223, 2097699, F3, 4, 18) (dual of [(2097699, 4), 8390573, 19]-NRT-code) | [i] | OOA Folding | |