Information on Result #906198
Linear OOA(3144, 4783133, F3, 2, 11) (dual of [(4783133, 2), 9566122, 12]-NRT-code), using (u, u+v)-construction based on
- linear OOA(316, 157, F3, 2, 5) (dual of [(157, 2), 298, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(31, 40, F3, 2, 1) (dual of [(40, 2), 79, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(31, s, F3, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(31, s, F3, 2, 1) for arbitrarily large s, using
- linear OOA(34, 40, F3, 2, 2) (dual of [(40, 2), 76, 3]-NRT-code), using
- appending kth column [i] based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- appending kth column [i] based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- linear OOA(311, 77, F3, 2, 5) (dual of [(77, 2), 143, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 11, 77)-net over F3, using
- linear OOA(31, 40, F3, 2, 1) (dual of [(40, 2), 79, 2]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(3128, 4782976, F3, 2, 11) (dual of [(4782976, 2), 9565824, 12]-NRT-code), using
- trace code [i] based on linear OOA(964, 2391488, F9, 2, 11) (dual of [(2391488, 2), 4782912, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(964, 4782976, F9, 11) (dual of [4782976, 4782912, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- 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(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(10) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(964, 4782976, F9, 11) (dual of [4782976, 4782912, 12]-code), using
- trace code [i] based on linear OOA(964, 2391488, F9, 2, 11) (dual of [(2391488, 2), 4782912, 12]-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(3144, 2391566, F3, 4, 11) (dual of [(2391566, 4), 9566120, 12]-NRT-code) | [i] | OOA Folding | |