Information on Result #808501
Linear OOA(2193, 527, F2, 2, 39) (dual of [(527, 2), 861, 40]-NRT-code), using OOA 2-folding based on linear OA(2193, 1054, F2, 39) (dual of [1054, 861, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(2193, 1055, F2, 39) (dual of [1055, 862, 40]-code), using
- construction XX applied to C1 = C([1019,32]), C2 = C([0,34]), C3 = C1 + C2 = C([0,32]), and C∩ = C1 ∩ C2 = C([1019,34]) [i] based on
- linear OA(2181, 1023, F2, 37) (dual of [1023, 842, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,32}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2166, 1023, F2, 35) (dual of [1023, 857, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2186, 1023, F2, 39) (dual of [1023, 837, 40]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,34}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2161, 1023, F2, 33) (dual of [1023, 862, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [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(21, 6, F2, 1) (dual of [6, 5, 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([1019,32]), C2 = C([0,34]), C3 = C1 + C2 = C([0,32]), and C∩ = C1 ∩ C2 = C([1019,34]) [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(2193, 515, F2, 3, 39) (dual of [(515, 3), 1352, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2193, 515, F2, 4, 39) (dual of [(515, 4), 1867, 40]-NRT-code) | [i] | ||
| 3 | Linear OOA(2193, 515, F2, 5, 39) (dual of [(515, 5), 2382, 40]-NRT-code) | [i] | ||
| 4 | Linear OOA(2193, 515, F2, 6, 39) (dual of [(515, 6), 2897, 40]-NRT-code) | [i] | ||
| 5 | Linear OOA(2193, 515, F2, 7, 39) (dual of [(515, 7), 3412, 40]-NRT-code) | [i] | ||
| 6 | Linear OOA(2193, 515, F2, 8, 39) (dual of [(515, 8), 3927, 40]-NRT-code) | [i] | ||
| 7 | Digital (154, 193, 515)-net over F2 | [i] | ||