Information on Result #1115662
Linear OOA(2146, 1677725, F2, 5, 13) (dual of [(1677725, 5), 8388479, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(27, 5, F2, 5, 6) (dual of [(5, 5), 18, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(5;F,18P) [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
- linear OOA(2139, 1677720, F2, 5, 13) (dual of [(1677720, 5), 8388461, 14]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2139, 8388600, F2, 13) (dual of [8388600, 8388461, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- OOA 5-folding [i] based on linear OA(2139, 8388600, F2, 13) (dual of [8388600, 8388461, 14]-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(2210, 3355450, F2, 5, 13) (dual of [(3355450, 5), 16777040, 14]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2146, 1677725, F2, 6, 13) (dual of [(1677725, 6), 10066204, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2146, 1677725, F2, 7, 13) (dual of [(1677725, 7), 11743929, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(2146, 1677725, F2, 8, 13) (dual of [(1677725, 8), 13421654, 14]-NRT-code) | [i] | ||
| 5 | Digital (133, 146, 1677725)-net over F2 | [i] | ||