Information on Result #702819
Linear OA(2158, 1060, F2, 31) (dual of [1060, 902, 32]-code), using construction XX applied to C1 = C([1019,24]), C2 = C([0,26]), C3 = C1 + C2 = C([0,24]), and C∩ = C1 ∩ C2 = C([1019,26]) based on
- linear OA(2141, 1023, F2, 29) (dual of [1023, 882, 30]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,24}, and designed minimum distance d ≥ |I|+1 = 30 [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(2121, 1023, F2, 25) (dual of [1023, 902, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [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
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 OA(2157, 1059, F2, 30) (dual of [1059, 902, 31]-code) | [i] | Truncation | |
| 2 | Linear OOA(2158, 530, F2, 2, 31) (dual of [(530, 2), 902, 32]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2158, 353, F2, 3, 31) (dual of [(353, 3), 901, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(2158, 265, F2, 4, 31) (dual of [(265, 4), 902, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(2158, 212, F2, 5, 31) (dual of [(212, 5), 902, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(2158, 176, F2, 6, 31) (dual of [(176, 6), 898, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(2158, 151, F2, 7, 31) (dual of [(151, 7), 899, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(2158, 132, F2, 8, 31) (dual of [(132, 8), 898, 32]-NRT-code) | [i] | ||