Information on Result #2783962
Linear OOA(2137, 131077, F2, 4, 14) (dual of [(131077, 4), 524171, 15]-NRT-code), using 1 step truncation based on linear OOA(2138, 131078, F2, 4, 15) (dual of [(131078, 4), 524174, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2138, 524312, F2, 15) (dual of [524312, 524174, 16]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2135, 524309, F2, 15) (dual of [524309, 524174, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(2134, 524288, F2, 15) (dual of [524288, 524154, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2115, 524288, F2, 13) (dual of [524288, 524173, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(220, 21, F2, 19) (dual of [21, 1, 20]-code), using
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- dual of repetition code with length 21 [i]
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- linear OA(21, 21, F2, 1) (dual of [21, 20, 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(14) ⊂ Ce(12) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(2135, 524309, F2, 15) (dual of [524309, 524174, 16]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(2137, 116482, F2, 5, 14) (dual of [(116482, 5), 582273, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2137, 116482, F2, 6, 14) (dual of [(116482, 6), 698755, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(2137, 116482, F2, 7, 14) (dual of [(116482, 7), 815237, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(2137, 116482, F2, 8, 14) (dual of [(116482, 8), 931719, 15]-NRT-code) | [i] | ||
| 5 | Digital (123, 137, 116482)-net over F2 | [i] | ||