Information on Result #702957
Linear OA(2213, 1060, F2, 43) (dual of [1060, 847, 44]-code), using construction XX applied to C1 = C([1019,36]), C2 = C([0,38]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([1019,38]) based on
- linear OA(2196, 1023, F2, 41) (dual of [1023, 827, 42]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,36}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2186, 1023, F2, 39) (dual of [1023, 837, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2206, 1023, F2, 43) (dual of [1023, 817, 44]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,38}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2176, 1023, F2, 37) (dual of [1023, 847, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [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(2212, 1059, F2, 42) (dual of [1059, 847, 43]-code) | [i] | Truncation | |
| 2 | Linear OOA(2213, 530, F2, 2, 43) (dual of [(530, 2), 847, 44]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2213, 353, F2, 3, 43) (dual of [(353, 3), 846, 44]-NRT-code) | [i] | ||
| 4 | Linear OOA(2213, 265, F2, 4, 43) (dual of [(265, 4), 847, 44]-NRT-code) | [i] | ||
| 5 | Linear OOA(2213, 212, F2, 5, 43) (dual of [(212, 5), 847, 44]-NRT-code) | [i] | ||
| 6 | Linear OOA(2213, 176, F2, 6, 43) (dual of [(176, 6), 843, 44]-NRT-code) | [i] | ||
| 7 | Linear OOA(2213, 151, F2, 7, 43) (dual of [(151, 7), 844, 44]-NRT-code) | [i] | ||