Information on Result #948422
Linear OOA(2259, 1375, F2, 3, 43) (dual of [(1375, 3), 3866, 44]-NRT-code), using OOA 3-folding based on linear OA(2259, 4125, F2, 43) (dual of [4125, 3866, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(2259, 4126, F2, 43) (dual of [4126, 3867, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(38) [i] based on
- linear OA(2253, 4096, F2, 43) (dual of [4096, 3843, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2229, 4096, F2, 39) (dual of [4096, 3867, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(42) ⊂ Ce(38) [i] based on
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(2259, 1375, F2, 3, 42) (dual of [(1375, 3), 3866, 43]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2260, 1375, F2, 3, 43) (dual of [(1375, 3), 3865, 44]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2259, 1375, F2, 4, 43) (dual of [(1375, 4), 5241, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2259, 1375, F2, 5, 43) (dual of [(1375, 5), 6616, 44]-NRT-code) | [i] | ||
| 5 | Linear OOA(2259, 1375, F2, 6, 43) (dual of [(1375, 6), 7991, 44]-NRT-code) | [i] | ||
| 6 | Linear OOA(2259, 1375, F2, 7, 43) (dual of [(1375, 7), 9366, 44]-NRT-code) | [i] | ||
| 7 | Linear OOA(2259, 1375, F2, 8, 43) (dual of [(1375, 8), 10741, 44]-NRT-code) | [i] | ||
| 8 | Digital (216, 259, 1375)-net over F2 | [i] | ||