Information on Result #703045
Linear OA(2257, 1065, F2, 51) (dual of [1065, 808, 52]-code), using construction XX applied to C1 = C([1019,44]), C2 = C([1,46]), C3 = C1 + C2 = C([1,44]), and C∩ = C1 ∩ C2 = C([1019,46]) based on
- linear OA(2236, 1023, F2, 49) (dual of [1023, 787, 50]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2225, 1023, F2, 46) (dual of [1023, 798, 47]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(2246, 1023, F2, 51) (dual of [1023, 777, 52]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,46}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2215, 1023, F2, 44) (dual of [1023, 808, 45]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(210, 31, F2, 4) (dual of [31, 21, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), using
- 1 times truncation [i] based on linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33 | 210−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), 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(2256, 1064, F2, 50) (dual of [1064, 808, 51]-code) | [i] | Truncation | |
| 2 | Linear OOA(2257, 213, F2, 5, 51) (dual of [(213, 5), 808, 52]-NRT-code) | [i] | OOA Folding | |