Information on Result #1119440
Linear OOA(3153, 4846384, F3, 5, 10) (dual of [(4846384, 5), 24231767, 11]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(319, 1490944, F3, 5, 3) (dual of [(1490944, 5), 7454701, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(319, 1490944, F3, 3, 3) (dual of [(1490944, 3), 4472813, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(319, 1490944, F3, 2, 3) (dual of [(1490944, 2), 2981869, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(319, 1490944, F3, 3) (dual of [1490944, 1490925, 4]-code or 1490944-cap in PG(18,3)), using
- appending kth column [i] based on linear OOA(319, 1490944, F3, 2, 3) (dual of [(1490944, 2), 2981869, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(319, 1490944, F3, 3, 3) (dual of [(1490944, 3), 4472813, 4]-NRT-code), using
- linear OOA(343, 1677720, F3, 5, 5) (dual of [(1677720, 5), 8388557, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(343, 2391491, F3, 5, 5) (dual of [(2391491, 5), 11957412, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(329, 4782969, F3, 4) (dual of [4782969, 4782940, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- discarding factors / shortening the dual code based on linear OOA(343, 2391491, F3, 5, 5) (dual of [(2391491, 5), 11957412, 6]-NRT-code), using
- linear OOA(391, 1677720, F3, 5, 10) (dual of [(1677720, 5), 8388509, 11]-NRT-code), using
- OOA 5-folding [i] based on linear OA(391, 8388600, F3, 10) (dual of [8388600, 8388509, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- OOA 5-folding [i] based on linear OA(391, 8388600, F3, 10) (dual of [8388600, 8388509, 11]-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(3153, 4846383, F3, 15, 10) (dual of [(4846383, 15), 72695592, 11]-NRT-code) | [i] | OOA Stacking with Additional Row | |