Information on Result #1706403
Linear OOA(2251, 3305872, F2, 8, 16) (dual of [(3305872, 8), 26446725, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2251, 3305872, F2, 2, 16) (dual of [(3305872, 2), 6611493, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2251, 4227078, F2, 2, 16) (dual of [(4227078, 2), 8453905, 17]-NRT-code), using
- strength reduction [i] based on linear OOA(2251, 4227078, F2, 2, 17) (dual of [(4227078, 2), 8453905, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(266, 32777, F2, 2, 8) (dual of [(32777, 2), 65488, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(266, 65554, F2, 8) (dual of [65554, 65488, 9]-code), using
- strength reduction [i] based on linear OA(266, 65554, F2, 9) (dual of [65554, 65488, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(265, 65536, F2, 9) (dual of [65536, 65471, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(249, 65536, F2, 7) (dual of [65536, 65487, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(217, 18, F2, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
- dual of repetition code with length 18 [i]
- linear OA(21, 18, F2, 1) (dual of [18, 17, 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(266, 65554, F2, 9) (dual of [65554, 65488, 10]-code), using
- OOA 2-folding [i] based on linear OA(266, 65554, F2, 8) (dual of [65554, 65488, 9]-code), using
- linear OOA(2185, 4194301, F2, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2185, 8388602, F2, 17) (dual of [8388602, 8388417, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 2-folding [i] based on linear OA(2185, 8388602, F2, 17) (dual of [8388602, 8388417, 18]-code), using
- linear OOA(266, 32777, F2, 2, 8) (dual of [(32777, 2), 65488, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- strength reduction [i] based on linear OOA(2251, 4227078, F2, 2, 17) (dual of [(4227078, 2), 8453905, 18]-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(2251, 3305871, F2, 24, 16) (dual of [(3305871, 24), 79340653, 17]-NRT-code) | [i] | OOA Stacking with Additional Row | |