Information on Result #1051603
Linear OOA(2122, 32773, F2, 4, 14) (dual of [(32773, 4), 130970, 15]-NRT-code), using OOA 4-folding based on linear OA(2122, 131092, F2, 14) (dual of [131092, 130970, 15]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2120, 131090, F2, 14) (dual of [131090, 130970, 15]-code), using
- 1 times truncation [i] based on linear OA(2121, 131091, F2, 15) (dual of [131091, 130970, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(2120, 131072, F2, 15) (dual of [131072, 130952, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2103, 131072, F2, 13) (dual of [131072, 130969, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(218, 19, F2, 17) (dual of [19, 1, 18]-code), using
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- dual of repetition code with length 19 [i]
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- linear OA(21, 19, F2, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- 1 times truncation [i] based on linear OA(2121, 131091, F2, 15) (dual of [131091, 130970, 16]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(2123, 32773, F2, 4, 14) (dual of [(32773, 4), 130969, 15]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2124, 32773, F2, 4, 14) (dual of [(32773, 4), 130968, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(2122, 32773, F2, 5, 14) (dual of [(32773, 5), 163743, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2122, 32773, F2, 6, 14) (dual of [(32773, 6), 196516, 15]-NRT-code) | [i] | ||
| 5 | Linear OOA(2122, 32773, F2, 7, 14) (dual of [(32773, 7), 229289, 15]-NRT-code) | [i] | ||
| 6 | Linear OOA(2122, 32773, F2, 8, 14) (dual of [(32773, 8), 262062, 15]-NRT-code) | [i] | ||
| 7 | Digital (108, 122, 32773)-net over F2 | [i] | ||