Information on Result #1010896
Linear OOA(3230, 3188682, F3, 3, 17) (dual of [(3188682, 3), 9565816, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(318, 32, F3, 3, 8) (dual of [(32, 3), 78, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (10, 18, 32)-net over F3, using
- trace code for nets [i] based on digital (1, 9, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- trace code for nets [i] based on digital (1, 9, 16)-net over F9, using
- extracting embedded OOA [i] based on digital (10, 18, 32)-net over F3, using
- linear OOA(3212, 3188650, F3, 3, 17) (dual of [(3188650, 3), 9565738, 18]-NRT-code), using
- trace code [i] based on linear OOA(9106, 1594325, F9, 3, 17) (dual of [(1594325, 3), 4782869, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9106, 4782975, F9, 17) (dual of [4782975, 4782869, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(9106, 4782976, F9, 17) (dual of [4782976, 4782870, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(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(16) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(9106, 4782976, F9, 17) (dual of [4782976, 4782870, 18]-code), using
- OOA 3-folding [i] based on linear OA(9106, 4782975, F9, 17) (dual of [4782975, 4782869, 18]-code), using
- trace code [i] based on linear OOA(9106, 1594325, F9, 3, 17) (dual of [(1594325, 3), 4782869, 18]-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(3231, 3188682, F3, 3, 17) (dual of [(3188682, 3), 9565815, 18]-NRT-code) | [i] | OOA Duplication | |