Information on Result #1184760
Digital (213, 232, 1062885)-net over F3, using net defined by OOA based on linear OOA(3232, 1062885, F3, 21, 19) (dual of [(1062885, 21), 22320353, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3232, 3188656, F3, 3, 19) (dual of [(3188656, 3), 9565736, 20]-NRT-code), using
- trace code [i] based on linear OOA(9116, 1594328, F9, 3, 19) (dual of [(1594328, 3), 4782868, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9116, 4782984, F9, 19) (dual of [4782984, 4782868, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(9116, 4782986, F9, 19) (dual of [4782986, 4782870, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(93, 17, F9, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(9116, 4782986, F9, 19) (dual of [4782986, 4782870, 20]-code), using
- OOA 3-folding [i] based on linear OA(9116, 4782984, F9, 19) (dual of [4782984, 4782868, 20]-code), using
- trace code [i] based on linear OOA(9116, 1594328, F9, 3, 19) (dual of [(1594328, 3), 4782868, 20]-NRT-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, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (214, 233, 1062885)-net over F3 | [i] | Net Duplication | |
| 2 | Digital (213, 231, 1062885)-net over F3 | [i] | m-Reduction | |