Information on Result #947462
Linear OOA(2168, 353, F2, 3, 33) (dual of [(353, 3), 891, 34]-NRT-code), using OOA 3-folding based on linear OA(2168, 1059, F2, 33) (dual of [1059, 891, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2168, 1060, F2, 33) (dual of [1060, 892, 34]-code), using
- construction XX applied to C1 = C([1019,26]), C2 = C([0,28]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([1019,28]) [i] based on
- 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(2141, 1023, F2, 29) (dual of [1023, 882, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2161, 1023, F2, 33) (dual of [1023, 862, 34]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,28}, and designed minimum distance d ≥ |I|+1 = 34 [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(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, 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([1019,26]), C2 = C([0,28]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([1019,28]) [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(2168, 353, F2, 3, 32) (dual of [(353, 3), 891, 33]-NRT-code) | [i] | Strength Reduction for OOAs | |