Information on Result #1010631
Linear OOA(3160, 3188734, F3, 3, 12) (dual of [(3188734, 3), 9566042, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(318, 84, F3, 3, 6) (dual of [(84, 3), 234, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 18, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 6, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- trace code for nets [i] based on digital (0, 6, 28)-net over F27, using
- extracting embedded OOA [i] based on digital (12, 18, 84)-net over F3, using
- linear OOA(3142, 3188650, F3, 3, 12) (dual of [(3188650, 3), 9565808, 13]-NRT-code), using
- trace code [i] based on linear OOA(971, 1594325, F9, 3, 12) (dual of [(1594325, 3), 4782904, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(971, 4782975, F9, 12) (dual of [4782975, 4782904, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(971, 4782976, F9, 12) (dual of [4782976, 4782905, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(964, 4782969, F9, 11) (dual of [4782969, 4782905, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(971, 4782976, F9, 12) (dual of [4782976, 4782905, 13]-code), using
- OOA 3-folding [i] based on linear OA(971, 4782975, F9, 12) (dual of [4782975, 4782904, 13]-code), using
- trace code [i] based on linear OOA(971, 1594325, F9, 3, 12) (dual of [(1594325, 3), 4782904, 13]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3161, 3188734, F3, 3, 12) (dual of [(3188734, 3), 9566041, 13]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3160, 1594366, F3, 15, 12) (dual of [(1594366, 15), 23915330, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |