Information on Result #895237
Linear OOA(3212, 4194429, F3, 2, 18) (dual of [(4194429, 2), 8388646, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(332, 128, F3, 2, 9) (dual of [(128, 2), 224, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(332, 256, F3, 9) (dual of [256, 224, 10]-code), using
- construction X4 applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(331, 244, F3, 9) (dual of [244, 213, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 244 | 310−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(321, 244, F3, 7) (dual of [244, 223, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 244 | 310−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [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 C([0,4]) ⊂ C([0,3]) [i] based on
- OOA 2-folding [i] based on linear OA(332, 256, F3, 9) (dual of [256, 224, 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(3212, 2097214, F3, 4, 18) (dual of [(2097214, 4), 8388644, 19]-NRT-code) | [i] | OOA Folding | |