Information on Result #2788576
Linear OOA(2141, 32773, F2, 4, 16) (dual of [(32773, 4), 130951, 17]-NRT-code), using 22 times duplication based on linear OOA(2139, 32773, F2, 4, 16) (dual of [(32773, 4), 130953, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2139, 131092, F2, 16) (dual of [131092, 130953, 17]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2137, 131090, F2, 16) (dual of [131090, 130953, 17]-code), using
- 1 times truncation [i] based on linear OA(2138, 131091, F2, 17) (dual of [131091, 130953, 18]-code), using
- construction X4 applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2137, 131072, F2, 17) (dual of [131072, 130935, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(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(16) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(2138, 131091, F2, 17) (dual of [131091, 130953, 18]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2137, 131090, F2, 16) (dual of [131090, 130953, 17]-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(2141, 27540, F2, 5, 16) (dual of [(27540, 5), 137559, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2141, 27540, F2, 6, 16) (dual of [(27540, 6), 165099, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(2141, 27540, F2, 7, 16) (dual of [(27540, 7), 192639, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(2141, 27540, F2, 8, 16) (dual of [(27540, 8), 220179, 17]-NRT-code) | [i] | ||
| 5 | Digital (125, 141, 27540)-net over F2 | [i] | ||