Information on Result #1706683
Linear OOA(2254, 2839897, F2, 8, 17) (dual of [(2839897, 8), 22718922, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2254, 2839897, F2, 3, 17) (dual of [(2839897, 3), 8519437, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(269, 43696, F2, 3, 8) (dual of [(43696, 3), 131019, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(269, 131088, F2, 8) (dual of [131088, 131019, 9]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(269, 131090, F2, 8) (dual of [131090, 131021, 9]-code), using
- OOA 3-folding [i] based on linear OA(269, 131088, F2, 8) (dual of [131088, 131019, 9]-code), using
- linear OOA(2185, 2796201, F2, 3, 17) (dual of [(2796201, 3), 8388418, 18]-NRT-code), using
- OOA 3-folding [i] 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]
- OOA 3-folding [i] based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- linear OOA(269, 43696, F2, 3, 8) (dual of [(43696, 3), 131019, 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(2254, 2839896, F2, 24, 17) (dual of [(2839896, 24), 68157250, 18]-NRT-code) | [i] | OOA Stacking with Additional Row | |