Information on Result #807694
Linear OOA(2163, 537, F2, 2, 31) (dual of [(537, 2), 911, 32]-NRT-code), using OOA 2-folding based on linear OA(2163, 1074, F2, 31) (dual of [1074, 911, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2163, 1075, F2, 31) (dual of [1075, 912, 32]-code), using
- construction XX applied to C1 = C([1019,22]), C2 = C([0,26]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C([1019,26]) [i] based on
- linear OA(2131, 1023, F2, 27) (dual of [1023, 892, 28]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,22}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2131, 1023, F2, 27) (dual of [1023, 892, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2151, 1023, F2, 31) (dual of [1023, 872, 32]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,26}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2111, 1023, F2, 23) (dual of [1023, 912, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-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
- linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)) (see above)
- construction XX applied to C1 = C([1019,22]), C2 = C([0,26]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C([1019,26]) [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(2163, 537, F2, 3, 31) (dual of [(537, 3), 1448, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2163, 537, F2, 4, 31) (dual of [(537, 4), 1985, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(2163, 537, F2, 5, 31) (dual of [(537, 5), 2522, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(2163, 537, F2, 6, 31) (dual of [(537, 6), 3059, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(2163, 537, F2, 7, 31) (dual of [(537, 7), 3596, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(2163, 537, F2, 8, 31) (dual of [(537, 8), 4133, 32]-NRT-code) | [i] | ||
| 7 | Digital (132, 163, 537)-net over F2 | [i] | ||