Information on Result #1616072
Linear OOA(2220, 2097406, F2, 4, 16) (dual of [(2097406, 4), 8389404, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(236, 256, F2, 4, 8) (dual of [(256, 4), 988, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(236, 256, F2, 2, 8) (dual of [(256, 2), 476, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(236, 512, F2, 8) (dual of [512, 476, 9]-code), using
- 1 times truncation [i] based on linear OA(237, 513, F2, 9) (dual of [513, 476, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 513 | 218−1, 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(237, 513, F2, 9) (dual of [513, 476, 10]-code), using
- OOA 2-folding [i] based on linear OA(236, 512, F2, 8) (dual of [512, 476, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(236, 256, F2, 2, 8) (dual of [(256, 2), 476, 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
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(2220, 2097406, F2, 5, 16) (dual of [(2097406, 5), 10486810, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2220, 2097406, F2, 6, 16) (dual of [(2097406, 6), 12584216, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(2220, 2097406, F2, 7, 16) (dual of [(2097406, 7), 14681622, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(2220, 2097406, F2, 8, 16) (dual of [(2097406, 8), 16779028, 17]-NRT-code) | [i] | ||
| 5 | Digital (204, 220, 2097406)-net over F2 | [i] | ||