Information on Result #894360
Linear OOA(2258, 4325383, F2, 2, 16) (dual of [(4325383, 2), 8650508, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(274, 131082, F2, 2, 8) (dual of [(131082, 2), 262090, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(274, 262164, F2, 8) (dual of [262164, 262090, 9]-code), using
- strength reduction [i] based on linear OA(274, 262164, F2, 9) (dual of [262164, 262090, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(273, 262144, F2, 9) (dual of [262144, 262071, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(255, 262144, F2, 7) (dual of [262144, 262089, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(219, 20, F2, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
- dual of repetition code with length 20 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 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(8) ⊂ Ce(6) [i] based on
- strength reduction [i] based on linear OA(274, 262164, F2, 9) (dual of [262164, 262090, 10]-code), using
- OOA 2-folding [i] based on linear OA(274, 262164, F2, 8) (dual of [262164, 262090, 9]-code), using
- linear OOA(2184, 4194301, F2, 2, 16) (dual of [(4194301, 2), 8388418, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2184, 8388602, F2, 16) (dual of [8388602, 8388418, 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 2-folding [i] based on linear OA(2184, 8388602, F2, 16) (dual of [8388602, 8388418, 17]-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(2258, 4325383, F2, 3, 16) (dual of [(4325383, 3), 12975891, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2258, 4325383, F2, 4, 16) (dual of [(4325383, 4), 17301274, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(2258, 4325383, F2, 5, 16) (dual of [(4325383, 5), 21626657, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(2258, 4325383, F2, 6, 16) (dual of [(4325383, 6), 25952040, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(2258, 4325383, F2, 7, 16) (dual of [(4325383, 7), 30277423, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(2258, 4325383, F2, 8, 16) (dual of [(4325383, 8), 34602806, 17]-NRT-code) | [i] | ||
| 7 | Digital (242, 258, 4325383)-net over F2 | [i] | ||