Information on Result #1095633
Linear OOA(2170, 419435, F2, 5, 16) (dual of [(419435, 5), 2097005, 17]-NRT-code), using OOA 5-folding based on linear OA(2170, 2097175, F2, 16) (dual of [2097175, 2097005, 17]-code), using
- strength reduction [i] based on linear OA(2170, 2097175, F2, 17) (dual of [2097175, 2097005, 18]-code), using
- construction X4 applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2169, 2097152, F2, 17) (dual of [2097152, 2096983, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2148, 2097152, F2, 15) (dual of [2097152, 2097004, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(222, 23, F2, 21) (dual of [23, 1, 22]-code), using
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- dual of repetition code with length 23 [i]
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- linear OA(21, 23, F2, 1) (dual of [23, 22, 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
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(2171, 419435, F2, 5, 16) (dual of [(419435, 5), 2097004, 17]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2172, 419435, F2, 5, 16) (dual of [(419435, 5), 2097003, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(2173, 419435, F2, 5, 16) (dual of [(419435, 5), 2097002, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(2170, 419435, F2, 6, 16) (dual of [(419435, 6), 2516440, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2170, 419435, F2, 7, 16) (dual of [(419435, 7), 2935875, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(2170, 419435, F2, 8, 16) (dual of [(419435, 8), 3355310, 17]-NRT-code) | [i] | ||
| 7 | Digital (154, 170, 419435)-net over F2 | [i] | ||