Information on Result #1750758
Digital (97, 119, 531)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2119, 531, F2, 2, 22) (dual of [(531, 2), 943, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2119, 1062, F2, 22) (dual of [1062, 943, 23]-code), using
- strength reduction [i] based on linear OA(2119, 1062, F2, 23) (dual of [1062, 943, 24]-code), using
- adding a parity check bit [i] based on linear OA(2118, 1061, F2, 22) (dual of [1061, 943, 23]-code), using
- construction XX applied to C1 = C([1019,16]), C2 = C([1,18]), C3 = C1 + C2 = C([1,16]), and C∩ = C1 ∩ C2 = C([1019,18]) [i] based on
- linear OA(2101, 1023, F2, 21) (dual of [1023, 922, 22]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,16}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(290, 1023, F2, 18) (dual of [1023, 933, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2111, 1023, F2, 23) (dual of [1023, 912, 24]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,18}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(280, 1023, F2, 16) (dual of [1023, 943, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(26, 27, F2, 3) (dual of [27, 21, 4]-code or 27-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(21, 11, F2, 1) (dual of [11, 10, 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 XX applied to C1 = C([1019,16]), C2 = C([1,18]), C3 = C1 + C2 = C([1,16]), and C∩ = C1 ∩ C2 = C([1019,18]) [i] based on
- adding a parity check bit [i] based on linear OA(2118, 1061, F2, 22) (dual of [1061, 943, 23]-code), using
- strength reduction [i] based on linear OA(2119, 1062, F2, 23) (dual of [1062, 943, 24]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (98, 120, 531)-net over F2 | [i] | Net Duplication | |