Information on Result #2429155
Linear OOA(2254, 4259846, F2, 2, 16) (dual of [(4259846, 2), 8519438, 17]-NRT-code), using strength reduction based on linear OOA(2254, 4259846, F2, 2, 17) (dual of [(4259846, 2), 8519438, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(269, 65545, F2, 2, 8) (dual of [(65545, 2), 131021, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(269, 131090, F2, 8) (dual of [131090, 131021, 9]-code), using
- 1 times truncation [i] based on linear OA(270, 131091, F2, 9) (dual of [131091, 131021, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(269, 131072, F2, 9) (dual of [131072, 131003, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(252, 131072, F2, 7) (dual of [131072, 131020, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(218, 19, F2, 17) (dual of [19, 1, 18]-code), using
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- dual of repetition code with length 19 [i]
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- linear OA(21, 19, F2, 1) (dual of [19, 18, 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
- 1 times truncation [i] based on linear OA(270, 131091, F2, 9) (dual of [131091, 131021, 10]-code), using
- OOA 2-folding [i] based on linear OA(269, 131090, F2, 8) (dual of [131090, 131021, 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(269, 65545, F2, 2, 8) (dual of [(65545, 2), 131021, 9]-NRT-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(2254, 3879313, F2, 3, 16) (dual of [(3879313, 3), 11637685, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2254, 3879313, F2, 4, 16) (dual of [(3879313, 4), 15516998, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(2254, 3879313, F2, 5, 16) (dual of [(3879313, 5), 19396311, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(2254, 3879313, F2, 6, 16) (dual of [(3879313, 6), 23275624, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(2254, 3879313, F2, 7, 16) (dual of [(3879313, 7), 27154937, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(2254, 3879313, F2, 8, 16) (dual of [(3879313, 8), 31034250, 17]-NRT-code) | [i] | ||
| 7 | Digital (238, 254, 3879313)-net over F2 | [i] | ||