Information on Result #1117704
Linear OOA(3226, 1913192, F3, 5, 17) (dual of [(1913192, 5), 9565734, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(371, 1195745, F3, 5, 8) (dual of [(1195745, 5), 5978654, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(371, 4782980, F3, 8) (dual of [4782980, 4782909, 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
- OA 4-folding and stacking [i] based on linear OA(371, 4782980, F3, 8) (dual of [4782980, 4782909, 9]-code), using
- linear OOA(3155, 956596, F3, 5, 17) (dual of [(956596, 5), 4782825, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3155, 4782980, F3, 17) (dual of [4782980, 4782825, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3155, 4782983, F3, 17) (dual of [4782983, 4782828, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 1]-code) (see above)
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3155, 4782983, F3, 17) (dual of [4782983, 4782828, 18]-code), using
- OOA 5-folding [i] based on linear OA(3155, 4782980, F3, 17) (dual of [4782980, 4782825, 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(3227, 1913192, F3, 5, 17) (dual of [(1913192, 5), 9565733, 18]-NRT-code) | [i] | OOA Duplication | |