Information on Result #895215
Linear OOA(3237, 6585792, F3, 2, 17) (dual of [(6585792, 2), 13171347, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(371, 2391491, F3, 2, 8) (dual of [(2391491, 2), 4782911, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(371, 4782982, F3, 8) (dual of [4782982, 4782911, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(371, 4782983, F3, 8) (dual of [4782983, 4782912, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(371, 4782969, F3, 8) (dual of [4782969, 4782898, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(357, 4782969, F3, 7) (dual of [4782969, 4782912, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(371, 4782983, F3, 8) (dual of [4782983, 4782912, 9]-code), using
- OOA 2-folding [i] based on linear OA(371, 4782982, F3, 8) (dual of [4782982, 4782911, 9]-code), using
- linear OOA(3166, 4194301, F3, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3166, 8388602, F3, 17) (dual of [8388602, 8388436, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- OOA 2-folding [i] based on linear OA(3166, 8388602, F3, 17) (dual of [8388602, 8388436, 18]-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(3237, 3292896, F3, 3, 17) (dual of [(3292896, 3), 9878451, 18]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3237, 3292896, F3, 4, 17) (dual of [(3292896, 4), 13171347, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(3237, 2195264, F3, 5, 17) (dual of [(2195264, 5), 10976083, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(3237, 1646447, F3, 18, 17) (dual of [(1646447, 18), 29635809, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |