Information on Result #1705414
Linear OOA(2240, 2101187, F2, 8, 17) (dual of [(2101187, 8), 16809256, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2240, 2101187, F2, 4, 17) (dual of [(2101187, 4), 8404508, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(255, 4037, F2, 4, 8) (dual of [(4037, 4), 16093, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(255, 4037, F2, 2, 8) (dual of [(4037, 2), 8019, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(255, 4104, F2, 2, 8) (dual of [(4104, 2), 8153, 9]-NRT-code), using
- strength reduction [i] based on linear OOA(255, 4104, F2, 2, 9) (dual of [(4104, 2), 8153, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(255, 8208, F2, 9) (dual of [8208, 8153, 10]-code), using
- 1 times code embedding in larger space [i] based on linear OA(254, 8207, F2, 9) (dual of [8207, 8153, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(253, 8192, F2, 9) (dual of [8192, 8139, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(240, 8192, F2, 7) (dual of [8192, 8152, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(214, 15, F2, 13) (dual of [15, 1, 14]-code), using
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- dual of repetition code with length 15 [i]
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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 code embedding in larger space [i] based on linear OA(254, 8207, F2, 9) (dual of [8207, 8153, 10]-code), using
- OOA 2-folding [i] based on linear OA(255, 8208, F2, 9) (dual of [8208, 8153, 10]-code), using
- strength reduction [i] based on linear OOA(255, 4104, F2, 2, 9) (dual of [(4104, 2), 8153, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(255, 4104, F2, 2, 8) (dual of [(4104, 2), 8153, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(255, 4037, F2, 2, 8) (dual of [(4037, 2), 8019, 9]-NRT-code), using
- linear OOA(2185, 2097150, F2, 4, 17) (dual of [(2097150, 4), 8388415, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 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 4-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- linear OOA(255, 4037, F2, 4, 8) (dual of [(4037, 4), 16093, 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(2240, 2101186, F2, 24, 17) (dual of [(2101186, 24), 50428224, 18]-NRT-code) | [i] | OOA Stacking with Additional Row | |