Information on Result #1704086
Linear OOA(2224, 2097649, F2, 8, 16) (dual of [(2097649, 8), 16780968, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2224, 2097649, F2, 4, 16) (dual of [(2097649, 4), 8390372, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(240, 499, F2, 4, 8) (dual of [(499, 4), 1956, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(240, 499, F2, 2, 8) (dual of [(499, 2), 958, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(240, 512, F2, 2, 8) (dual of [(512, 2), 984, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(240, 1024, F2, 8) (dual of [1024, 984, 9]-code), using
- 1 times truncation [i] based on linear OA(241, 1025, F2, 9) (dual of [1025, 984, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025 | 220−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(241, 1025, F2, 9) (dual of [1025, 984, 10]-code), using
- OOA 2-folding [i] based on linear OA(240, 1024, F2, 8) (dual of [1024, 984, 9]-code), using
- discarding factors / shortening the dual code based on linear OOA(240, 512, F2, 2, 8) (dual of [(512, 2), 984, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(240, 499, F2, 2, 8) (dual of [(499, 2), 958, 9]-NRT-code), using
- linear OOA(2184, 2097150, F2, 4, 16) (dual of [(2097150, 4), 8388416, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- OOA 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- linear OOA(240, 499, F2, 4, 8) (dual of [(499, 4), 1956, 9]-NRT-code), using
Mode: 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(2224, 2097648, F2, 24, 16) (dual of [(2097648, 24), 50343328, 17]-NRT-code) | [i] | OOA Stacking with Additional Row | |