Information on Result #1117736
Linear OOA(3218, 1692485, F3, 5, 17) (dual of [(1692485, 5), 8462207, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(352, 14765, F3, 5, 8) (dual of [(14765, 5), 73773, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(352, 59060, F3, 8) (dual of [59060, 59008, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(352, 59061, F3, 8) (dual of [59061, 59009, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(351, 59049, F3, 8) (dual of [59049, 58998, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(341, 59049, F3, 7) (dual of [59049, 59008, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(311, 12, F3, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,3)), using
- dual of repetition code with length 12 [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 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 X4 applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(352, 59061, F3, 8) (dual of [59061, 59009, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(352, 59060, F3, 8) (dual of [59060, 59008, 9]-code), using
- linear OOA(3166, 1677720, F3, 5, 17) (dual of [(1677720, 5), 8388434, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3166, 8388600, F3, 17) (dual of [8388600, 8388434, 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 5-folding [i] based on linear OA(3166, 8388600, F3, 17) (dual of [8388600, 8388434, 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(3219, 1692485, F3, 5, 17) (dual of [(1692485, 5), 8462206, 18]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3220, 1692485, F3, 5, 17) (dual of [(1692485, 5), 8462205, 18]-NRT-code) | [i] | ||